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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...
2 months 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...
2 months 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...
2 months 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...
2 months 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 ...
2 months 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 : ...
2 months 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...
2 months 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...
2 months 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...
2 months 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...
2 months ago
Solved
Laws of motion 4
Given the initial velocity 'u', final velocity 'v' and acceleration 'a', find the distance travelled.
2 months ago
Solved
Simulate full-stop emergency braking scenario.
Emergency braking events demand rapid deceleration to bring the vehicle safely to rest. Given initial vehicle speed and constant...
2 months ago
Solved
Compute optimal regenerative and friction brake torque blending.
Electric and hybrid vehicles combine regenerative braking with traditional friction braking to maximize energy recovery while en...
2 months ago
Solved
Estimate brake disc temperature rise during braking.
During braking, kinetic energy is converted into thermal energy, causing brake discs to heat up. Excessive temperature rise can ...
2 months ago
Solved
Compute optimal front–rear brake force distribution.
Modern braking systems dynamically distribute braking forces between front and rear axles to maintain stability, reduce stopping...
2 months ago
Solved
Compute wheel slip ratio during braking.
During braking, a difference develops between the vehicle’s forward speed and the rotational speed of its wheels. This differenc...
2 months ago
Solved
Estimate dynamic load transfer to front axle during braking.
During braking, load shifts from the rear axle to the front axle. Given mass, deceleration, center of gravity height, and wheelb...
2 months ago
Solved
Estimate brake line pressure required for a given force.
Hydraulic braking systems amplify pedal input to generate braking force. Given braking force and piston area, compute the hydrau...
2 months ago
Solved
Compute the required brake torque at wheel to stop the car
Brake torque defines how effectively braking force translates into wheel deceleration. Given braking force and wheel radius, det...
2 months ago
Solved
Compute braking force using vehicle mass and acceleration.
Compute braking force required to stop a vehicle of mass 'm' and with acceleration 'a' Remember: F = m × a.
2 months ago
Solved
Compute vehicle stopping distance using initial speed and constant deceleration.
Given vehicle speed v (m/s) and constant deceleration a (m/s²), compute stopping distance Remember: d = v² / (2a)
2 months 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...
2 months ago
