Find the smallest number that can be expressed as the sum of two (nonzero) perfect squares in two different ways.
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And what if the two perfect squares must be nonzero, positive, and different?
The smallest number that can be expressed as the sum of two (nonzero) perfect squares in
two different ways is
50:
1^{2} + 7^{2} and
5^{2} + 5^{2}.
The smallest number that can be expressed as the sum of two
different (nonzero) perfect squares
in
two different ways is
65:
1^{2} + 8^{2} and
4^{2} + 7^{2}.
The smallest number that can be expressed as the sum of two (nonzero) perfect squares in
three different ways is
425:
5^{2} + 20^{2},
8^{2} + 19^{2} and
13^{2} + 16^{2}.

Posted by Dej Mar
on 20080925 04:39:57 