If an Even number could be expressed in the form a² + b² . And if there exits two other numbers m,n such that
a² + b² = m² + n²
then , my question is
is there any relation between (a,b) and (m,n) apart from a² + b² = m² + n² ??
If an Even number could be expressed in the form a² + b² . And if there exits two other numbers m,n such that
a² + b² = m² + n²
then , my question is
is there any relation between (a,b) and (m,n) apart from a² + b² = m² + n² ??
The condition for an integer x to be a sum of two squares in more than one way is that x should have at least two prime factors of the form 4k+1. For example, , and , with both 5 and 13 being a multiple of 4 plus 1. But there is no particular relation between the pairs of numbers (1,8) and (4,7) occurring in those decompositions.
Hello, ssnmanikanta!
There is an interesting theorem that may or may not help . . .
If a number is of the form , the product of two sums of squares,
. . then can be expressed as the sum of two squares in two ways.
. .