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Easy Sequences 40: Quadratic Congruence
Quadratic Congruence is a modular equation of the form: . In this exercise you will be given a vector containing the coefficie...

3 days ago

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Easy Sequences 16: Volume of Embedded Octahedron
An octahedron (not regular) is formed by joining the centers of the faces of a rectangular parallelepiped (see below figure). ...

10 days ago

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Easy Sequences 30: Nearly Pythagorean Triangles
A Nearly Pythagorean Triangle (abbreviated as "NPT'), is an integer-sided triangle whose square of the longest side, which we wi...

10 days ago

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Easy Sequences 27: Product of Radicals of Integers
The radical of a positive integer is defined as the product of the distinct prime numbers dividing . For example, the distinct ...

11 days ago

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List the cuban primes
The number 61 is a cuban prime because it is prime and the difference two cubes, 64 and 125. Write a function to list the cuba...

11 days ago

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Easy Sequences 35: Cutting a donut to Semi-prime pieces
The figure below illustrates how a torus (donut shape) can be cut in pieces with only cuts: ...

14 days ago

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Easy Sequences 37: Natural Factorable Polynomials
A polynomial of the form: , for , is said to be natural factorable if it can be factored into products of first degree binomials...

14 days ago

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Easy Sequences 36: Hyperbolic Lattice Points
The graph, shown below, of the hyperbola: , passes through four positive lattice points:. ...

15 days ago

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Easy Sequences 22: Sum of Proper Fractions
Let 'F' be the set of all proper fractions in lowest term, whose denominator is less than or equal 'd'. So, for d = 10, we have:...

16 days ago

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Easy Sequences 28: Sum of Radicals of Integers
The radical of a positive integer is defined as the product of the distinct prime numbers dividing . For example, the distinct ...

17 days ago

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Easy Sequences 29: Odd proper divisors of odd proper divisors
The number is special. It has odd number of proper divisors: . Furthermore, if you take any of its proper divisors, say , it t...

17 days ago

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Easy Sequences 33: Web Trapped Ant
An ant is trapped on a spider web inside a can with open top. The can has a radius and height . A spider sitting on the outside...

18 days ago

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List modest numbers up to n
After determining the nude numbers, or the numbers that openly display some of their divisors as their digits, one would think t...

23 days ago

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Easy Sequences 21: Combinatorial Summations
Create the function S(n), defined by the following summation: The symbol is the combination f...

23 days ago

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Easy Sequences 31: N-N's Sequence
We define the N-N's Sequence, as the series of all positive integers in ascending order and with repetition, wherein a appears ...

23 days ago

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Easy Sequences 25: Product of Series
The function 'P(n)' is defined as the series product: where 'T(n)' is the triangular sum: ...

26 days ago

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Easy Sequences 23: Hat Guessing Game!
Consider the following Game Show: Hats, with numbers written on each, were placed on the heads of the participants. Participant...

26 days ago

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Multiply binary numbers
Write a function to multiply two binary numbers input as strings. For example, input values of ‘1011’ and ‘101’ should give ’110...

27 days ago

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Count the primes in Collatz sequences
Several Cody problems (21, 69, 42937, 44448, 44784, 52422) involve Collatz sequences. These start with a seed . If is odd, the ...

1 month ago

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List the Moran numbers
The quotient of a Moran number and its digit sum is prime. For example, 117 and 481 are Moran numbers because 117/(1+1+7) is 13 ...

1 month ago

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Easy Sequences 6: Coefficient sums of derivatives
Consider the polynomial function and its first-order derivative . The sums of the coefficients of P and P', are and , respecti...

2 months ago

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Determine whether a number is a fibodiv number
The number 14 is a fibodiv number because you can divide it into 1 and 4, use those numbers as the seeds for a Fibonacci sequenc...

2 months ago

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Determine whether a number is unprimeable
The number 204 is unprimeable because no single digit can be changed to make it prime. In contrast, the number 207 is not unprim...

2 months ago

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Count the ways to draw non-intersecting chords between points on a circle
There are 9 ways to draw non-intersecting chords between four points on the perimeter of a circle (including no chords at all). ...

2 months ago

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Find the nth nude number
The number 672 is a nude number because it openly displays three of its divisors: 6, 7, and 2. In other words, a nude number is ...

2 months ago

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Easy Sequences 9: Faithful Pairs
A "faithful number" is a non-prime number that is one less or one more than some prime number but not both. For example, for num...

2 months ago

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Easy Sequences 10: Sum of Cumsums of Fibonacci Sequence
The function F(n) is defined as the set of Fibonacci numbers from the first up to the n-th. S(n) is the result of applying to F,...

2 months ago

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Easy Sequences 8: Triangles with integer sides and prime perimeters
The triangle below is special. It has integer sides and a prime perimeter. Given an integer "n" we want to know how many t...

2 months ago

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Hoax Numbers
A Hoax Number (OEIS A019506) is defined as a composite number, whose sum of digits is equal to the sum of digits of its distinct...

2 months ago

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Easy Sequences 3: Prime 44-number Squares
The positive integers 62 and 238 are related. Their squares (3844 and 56,644) both end in '44'. In fact, 62 and 238 are the 3rd ...

2 months ago

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