Solved

Sum of series
a(n) = n^2 - (n-1)^2 find the summation of the series upto n i.e. a(1)+a(2)+...+a(n)

12 months ago

Solved

Check the integers decomposition conjecture
Problem statement A conjecture (I rediscovered ?) related to Goldbach's one states that every integer above 2 can be written ...

12 months ago

Solved

Check the 'golden prime squares' equation
Historical context In december 2023, I / Nicolas Douillet was working on prime squares properties and I found* the formula : ...

12 months ago

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Euclid primes
Historical context Euclid, the greek mathematician proved at his time that the prime numbers set is an infinite. By the way he ...

12 months ago

Solved

Fermat primes
Historical context The french mathematician Pierre de Fermat found the formula to find some prime numbers. He thought / co...

12 months ago

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Ulam primes first formula
Historical context The polish-american mathematician Stanislaw Ulam found the formula to give the first 760 prime numbers ...

12 months ago

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Ulam primes second formula
Historical context The polish-american mathematician Stanislaw Ulam found the formula to give some prime numbers not given...

12 months ago

Solved

Euler primes
Historical context The great swiss mathematician Leonhard Euler found the formula to give some prime numbers. Problem...

12 months ago

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Frequencies of prime gaps
Problem statement Given two positive integers n and , write a function which computes the frequency of the gap between two ...

12 months ago

Solved

Find the first occurence of a given gap between two consecutive prime numbers
Problem statement Given a gap = p' - p between the two consecutive prime numbers p and p', find its first occurence, f. E...

1 year ago

Solved

Prime numbers which are the difference of two consecutive cubes
Problem statement Given a positive integer n greater than 2, find the prime numbers less or equal to n and which are the diff...

1 year ago

Solved

Estimating Monthly Electricity Cost for a Household Appliance
You recently bought an electric kettle for your kitchen, and you want to estimate how much it costs to run every month. The kett...

1 year ago

Solved

Voltage Divider Calculation
A voltage divider is a simple circuit used to obtain a reduced voltage from a higher voltage source using two resistors in serie...

1 year ago

Solved

LED Current Calculation
In an electrical circuit, the current (III) flowing through an LED is determined using Ohm’s Law: Where: I is the current ...

1 year ago

Solved

Inductor Energy Storage Calculation
The energy (EEE) stored in an inductor is given by the formula: Where: E is the energy in joules (J) L is the inductance in...

1 year ago

Solved

Calculate Charge Using Capacitance and Voltage
The charge (Q) stored in a capacitor is given by the formula:Q=C×V where: C is the capacitance (in farads) V is the voltage (...

1 year ago

Solved

Energy Stored in a Capacitor
The energy (E) stored in a capacitor is given by the formula: where: C is the capacitance (in farads) V is the voltage (in ...

1 year ago

Solved

Calculate Current in a Series Circuit Using KVL
Kirchhoff's Voltage Law (KVL) states that the sum of voltages around a closed loop is zero. Given a voltage source (V) and three...

1 year ago

Solved

Calculating the Total Resistance in a Series Circuit
Description: In a series circuit, the total resistance is the sum of the individual resistances. This problem asks you to write ...

1 year ago

Solved

Simple Electrical Power Calculation
Calculate the electrical power using the formula: P=V×I where: V is the voltage (in volts) I is the current (in amperes)

1 year ago

Solved

Ohm’s Law - Calculate Resistance
Ohm’s Law states that resistance R can be calculated as:R=V/I where: V is the voltage (in volts) I is the current (in ampere...

1 year ago

Solved

String Logic 10
Examples: 'SUNDAY' --> 83 'MONDAY' --> 77 'TUESDAY' --> 84 'WEDNESDAY' --> 87 'THURSDAY' --> 84 'FRIDAY' --> 70 'SATURD...

1 year ago

Solved

String Logic 5
Example: 'CAT' --> 'TAC' 'DOG' --> 'GOD' 'MATLAB' --> 'BALTAM' 'ROSY' --> 'YSOR' 'TRUST' --> 'TSURT' 'MOSTLY' --> 'YLTS...

1 year ago

Solved

String Logic 8
Example: 'CAT' --> 65 'DOG' --> 68 'ROSY' --> 79 'MATLAB' --> 65 'TRUST' --> 82 'MOSTLY' --> 76

1 year ago

Solved

String Logic 9
Examples: 'CAT' --> 'C' 'DOG' --> 'G' 'ROSLY' --> 'R' 'PROBLEM' --> 'M' 'TRUST' --> 'T' 'BASIC' --> 'C' 'GIANT' --> 'I'...

1 year ago

Solved

String Logic 12
Examples: 'CAT' --> 'ACT' 'DOG' --> 'DGO' 'ROSY' --> 'ORSY' 'MOSTLY' --> 'LMOSTY'

1 year ago

Solved

String Logic 15
Examples: 'CAT' --> 'XZG' 'DOG' --> 'WLT' 'ROSY' --> 'ILHB' 'MOSTLY' --> 'NLHGOB'

1 year ago

Solved

String Logic 11
Examples: 'SUNDAY' --> 6 'MONDAY' --> 6 'TUESDAY' --> 7 'WEDNESDAY' --> 9 'THURSDAY' --> 8 'FRIDAY' --> 5 'SATURDAY' --...

1 year ago

Solved

Remove Lower Case Letters
Example MEMOry --> MEMO IMPlEMeNtATiON --> IMPEMNATON

1 year ago

Solved

Remove Upper Case Letters
Example Matlab --> atlab proBlem --> prolem Enter --> nter

1 year ago