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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)

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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 ...

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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 : ...

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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 ...

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

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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 ...

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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...

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

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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 ...

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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...

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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...

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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...

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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...

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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 ...

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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...

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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 (...

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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 ...

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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...

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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 ...

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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)

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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...

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

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

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

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

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

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

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

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

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

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