Problema Solution
If m and n represent positive integers, then 2m always represents a positive even integer, and 2n+1 always represents a positive odd integer. Express the forms of all possible sums of squares of 2 positive integers using this fact
Answer provided by our tutors
sums of squares of 2 positive integers could be:
sum of an odd number squared plus an even number squared
sum of two odd numbers squared
sum of two even numbers squared
so there are three possibilities:
(2n+1)^2 + 2m^2 = 4n^2 + 4n + 2m^2 + 1
(2n+1)^2 + (2n+1)^2 = 8n^2 + 8n + 2
2m^2 + 2m^2 = 4m^2