Odd = Even?
Yes or No (or Ambiguous )
Is it True that every sum of four distinct odd squares is the sum of four distinct even squares?
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1 solution
W. Gosper conjectured that every sum of four distinct odd squares is the sum of four distinct even squares. This conjecture was proved by M. Hirschhorn using the identity ( 4 a + 1 ) 2 + ( 4 b + 1 ) 2 + ( 4 c + 1 ) 2 + ( 4 d + 1 ) 2 = 4 [ ( a + b + c + d + 1 ) 2 + ( a − b − c + d ) 2 + ( a − b + c − d ) 2 + ( a + b − c − d ) 2 ] where a , b , c and d are positive or negative integers.