Maths Olympiad Daily Problems

Reminder: You can you have time till 25JAN, if you think you have a correct solution, please post it here(in discussion) itself and ping @OGOsanskar_2. If your soln is correct you will be rewarded.

Well it’s Kel here VERY NOOB Can we proved that for p,q>3 there exist no solution As I have found one solution which is (2,5)

Find the number of solutions to the equation a + b + c + d = 50 if each variable is an even integer (including 0) and less than or equal to 22.

as said, you have time till 25 Jan, ones who will solve this correctly or partially will get prize.(Justification and full solution needed)

4/(3+2√2)

Find all functions f : N --> N satisfying the following conditions : - f is completely multiplicative , that is , for any two positive integers m , n : f(mn) = f(m)f(n) - There are infinitly many values for n such that (f(1),f(2),...,f(n)) is a permutation on (1 , 2 , ... , n)

Find all functions f : N --> N satisfying the following conditions : - f is completely multiplicative , that is , for any two positive integers m , n : f(mn) = f(m)f(n) - There are infinitly many values for n such that (f(1),f(2),...,f(n)) is a permutation on (1 , 2 , ... , n)

Try this

Tryy

Come in discussion

From now on, I will share one problem/week . You will have 1 week to solve it. Those who solve it correctly will be awarded.

also dont chat here