You should be able to solve this problem (standard for primary school students in my country where people poo in the...

You should be able to solve this problem (standard for primary school students in my country where people poo in the loo)

Attached: brainlet_prob.png (809x248, 15K)

maybe something about the lhs being even, so n=2k, so the rhs is 4k*(k+1)
didn't get further yet

Suppose equality holds, then clearly m>n. Rearrange equality:
(m+n-1)(m-n)=n
But m-n≥1 and m+n-1>n, Contradiction.

>doing proofs in elementary school
no

Sorry meant (m+n+1)(m-n)=n.

If equation holds m divides n or n+2, so n =km or n+2= km for some positive integer k bigger than or equal to 2. Substitute and get a quadratic equation with variable k that has no real solution. Rule out any easy cases with small n and m if necessary

>m divides n or n+2

That's true if m is prime. What about when m is not prime?

thanks user you are correct i have goofed. You could probably do some brute force with products of primes. It works for m=pq, each prime. Better argument more or less copying is that m > n but m < n+2 so m = n+1 which will never work

m = n = 0 works actually.

positive integers