Consecutive integers

Question

One integer is less than another. The sum of their squares is . Find the integers

Answer 1

Their sum of squares = square of the hypotenuse of a right triangle

b^2 + a^ = h^2

square the base add the square of the altitude = square of the hypotenuse

If it's not a 90 - 45 - 45 angle right triangle, then b doesn't = a and one side will be smaller than the other

common integer combinations are 3-4-5 or 5-12-13

3^2 + 4^2 = 5^2, 9+16 =25

5^2 + 12^2 = 13^2, 25+144 + 169

but there are an infinite number of such combinations