Problem 56393. Easy Sequences 77: Powers of Fibonacci Numbers

Created by Ramon Villamangca

Solve Later

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<div style = "text-align: start; line-height: 20.440001px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; "><div style="block-size: 172px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 86px; transform-origin: 407px 86px; vertical-align: baseline; "><div style="block-size: 47px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 23.5px; text-align: left; transform-origin: 384px 23.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">Given integers<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> x<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> and<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">, we are asked to evaluate the following function: <img src="data:image/png;base64,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" width="82" height="25" style="width: 82px; height: 25px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">. That is, P<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> equals<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> x<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> raised to the power of the<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> n<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">-th<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> <a target='_blank' href = "https://en.wikipedia.org/wiki/Fibonacci_number">Fibonacci number</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">. We define <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB4AAAAoCAYAAADpE0oSAAAAAXNSR0IArs4c6QAAAERlWElmTU0AKgAAAAgAAYdpAAQAAAABAAAAGgAAAAAAA6ABAAMAAAABAAEAAKACAAQAAAABAAAAHqADAAQAAAABAAAAKAAAAADkIHojAAACKklEQVRYCe2VwUsVURTGX6UhoeiDsFe4cBGC4FaJohZBCAVB2EKifX9ABLryLQQXIrhoEbQNXClCJBHkQjdSmwgqbBUPQ4JaRBAt0vp9OEcuw5k3M83rBTEHvnfOfPfc8825c+99lUpp5Qr8bytwJKWhR4xfA2l5Xpl7kA+9AXEdSQMRfxtfBavgUsTJbYI18BWoRg8YAhfAWSDbPXDFfu8z/VeEb3gJeaaXeAKUe8pLMO6oBSl+JBhfJ5a4Zz8htToN8MlLMC6L8AmSz9kE/NMg9sJ9yJfeQF7uKhNsmeUHMxQ4lpaTpePxoMg28YfgWWENfAa9eohsz4IiXmLW8WKskF58CbyI8amPacdpkAo6JmbaMGNAu3oY3ACXwRRoqd2hmnXbzNvZbZn4SiC8QTwKLgJ1Wgc6Pq9BS02fQTeTdXrXqf4ObsbhC1HqzETlw0vECn9J4G1cvg+oVmabJdOEPzqztKOnHT5OLUOozvlwQJOTLDy/z5wk3VBzDh+nGhC6Yr/HB7znk5C6BKzjSS8pB6f9kslukWWi6kwvUsQ6s05+TqIJv8k6KZZX51l/KDvgAUi162SYqPwuaPrfmlCxC/4xUI2bCTmH9PsoMRRWrO/9J52/ZZ4umSpomw2gpJfe8hSbHScvPw93JUr2jmLlnwnn6SBvrm473fXHwUR88t/quB+hM+AVmAc10BbrRuUH0I5eaItiIHKauOiNF5Qrw3IFyhVIWIHfT3Nv2j0vGNUAAAAASUVORK5CYII=" width="15" height="20" style="width: 15px; height: 20px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> as follows: <img src="data:image/png;base64,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" width="76" height="20" style="width: 76px; height: 20px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> and <img src="data:image/png;base64,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" width="100.5" height="20" style="width: 100.5px; height: 20px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> for <img src="data:image/png;base64,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" width="33.5" height="18" style="width: 33.5px; height: 18px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">.</div><div style="block-size: 25px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 12.5px; text-align: left; transform-origin: 384px 12.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> Example: <img src="data:image/png;base64,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" width="162" height="25" style="width: 162px; height: 25px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">.</div><div style="block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">Please reduce the output, modulo <img src="data:image/png;base64,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" width="93.5" height="20" style="width: 93.5px; height: 20px;"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">.</div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">------------------------</div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; ">HINT:<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "> One solution is already shown, however java math is not allowed.</div></div></div>

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5 Solutions
3 Solvers

Last Solution submitted on Feb 19, 2023

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3 Comments

3 Comments

David Hill on 19 Oct 2022

Test 10 is wrong. I ran your algorithm using java math and obtained:
s=[1021322 1048348 1452207 670027] which is the same figures I obtained using my algorithm. My algorithm passes all the other tests.

Ramon Villamangca on 20 Oct 2022

Hi David, I have not accounted for Fibonacci of 0 which is 0, which is required in my algorithm. Please try again.

GeeTwo on 17 Dec 2022

Surprisingly easy once you see a couple of tricks.

Solution Comments

Solution 10173822

2 Comments

2 Comments

GeeTwo on 20 Dec 2022

I know this solution has a higher Cody score than my previous, but it only takes one line of 75 characters (excluding endline), and I couldn't resist. This problem is THAT simple. It uses only five variables - including inputs and outputs, and all are scalars -- and nothing language specific besides how functions and for loops are defined and mod(), which essentially all languages define or at least support. And, of course, a couple of theorems.

No strings, str2num,regex, or any other tricks to make it seem simpler than it is! See the previous solution for a few comments that help a bit identifying the theorems.

Ramon Villamangca on 20 Dec 2022

That’s why it’s called “Easy…”

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Problem 56393. Easy Sequences 77: Powers of Fibonacci Numbers

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Problem 56393. Easy Sequences 77: Powers of Fibonacci Numbers

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