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Solved
Calculate the average value of the elements in the array
Calculate the average value of the elements in the array
20 days ago
Solved
the average value of the elements
Calculate the average value of the elements in the array
20 days ago
Solved
Linear primes p' = mp + n
Problem statement List the prime numbers of the form p' = mp + n for a given (m,n) couple and such that p' < k, k positive in...
20 days ago
Solved
List the complementary / symetric prime couples
Problem statement For a given positive integer n, provide the prime couples (p,p') such that p + p' = 10^n. NB : a number li...
20 days ago
Solved
Check Legendre's conjecture
Context and problem statement Legendre's conjecture states for a given positive integer n, there always exists at least one pri...
20 days ago
Solved
List the twin prime couples
Problem statement The twin prime couples (p,p') are the ones such that p' = p + 2. For a given integer n > 1, list the twin p...
20 days ago
Solved
Check Bertrand-Chebyshev's theorem about prime numbers
Historical context Bertrand's postulate, also later known as Chebyshev's theorem, is a very important theorem in number theory ...
20 days ago
Solved
Check p = 6n +/- 1, the generic formula for odd prime numbers greater than 3
Problem statement For all odd prime number p greater than 3, there exists a positive integer n, such that p = 6n +/- 1 : ...
20 days ago
Solved
Check p = 4n +/- 1, the generic formula for odd prime numbers
Problem statement For all odd prime number p, there exists a positive integer n, such that p = 4n +/- 1 : Check this f...
20 days ago
Solved
Chek the Delta = p' - p = 6k gap theorem about arithmetic progressions in the prime number set
Context In the prime numbers set there are some arithmetic progressions (sequences of three or more consecutive prime number...
20 days ago
Solved
List the near-square primes, p = n² + 1 (Landau's 4th problem)
Historical context At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about prime...
20 days ago
Solved
List primes which are the sum of two consecutive lower primes plus minus one
Problem statement Some prime numbers can be written as the sum of two consecutive lower primes plus / minus one : Like t...
21 days ago
Solved
Estimating Battery Lifetime Based on Load Profile and Depth of Discharge (DoD)
In a Battery Management System (BMS), the lifetime of a battery depends on various factors, including the Depth of Discharge (Do...
21 days ago
Solved
Estimating the Range of an Electric Vehicle (EV)
In Electric Vehicles (EVs), the driving range is the estimated distance a vehicle can travel on a fully charged battery. The ran...
21 days ago
Solved
Estimating Battery Backup Time for an Inverter
In a Battery Management System (BMS), estimating the backup time of a battery-powered inverter helps determine how long it can s...
21 days ago
Solved
Battery Charge Rate Calculation
In a Battery Management System (BMS), the charge rate () of a battery can be calculated using the formula: where: is th...
21 days ago
Solved
Battery State of Health (SoH) Calculation
In a Battery Management System (BMS), the State of Health (SoH) of a battery is an indicator of its overall condition. It is cal...
21 days ago
Solved
Battery Charge Efficiency Calculation
In a Battery Management System (BMS), the efficiency of battery charging can be estimated using the formula: where: is the...
21 days ago
Solved
Battery Voltage Drop Estimation
In a Battery Management System (BMS), the voltage drop (V_drop) due to the load can be calculated using the formula:V_drop=I×R ...
21 days ago
Solved
Battery Discharge Time Estimation
In a Battery Management System (BMS), the estimated discharge time (T) of a battery can be calculated as: where: is the ...
21 days ago
Solved
State of Charge (SoC) Estimation for a Battery
The State of Charge (SoC) of a battery represents its remaining charge as a percentage. It can be calculated using the formula: ...
21 days ago
Solved
Battery Life Estimation for a Device
A battery-powered device consumes a constant current while operating. The estimated battery life (T) can be calculated using the...
21 days 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...
21 days 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...
21 days 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 ...
21 days 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...
21 days ago
