and then zeros at the end.
22. Suppose that m, n are positive integers
2.7
(a) Find all positive integer solutions to the equation $m^2 - n^2 = 56$.
$(m^2 - n^2) = (m - n)(m + n) = 23(7)$. Notice that both $(m - n)$ and
$(m + n)$ are either even or odd. We also have $m - n < m + n$. Based
on these facts, we need to consider all the cases:
$(m - n) = 2$, $m + n = 28$, Or $(m - n) = 4$, $m + n = 14$. The solution
for $(m - n) = 2$, $m + n = 28$ is $m = 15$, $n = 13$. The solution for
$(m - n) = 4$, $m + n = 14$ is $m = 9$ and $n = 5$.
(b) Find all positive integer solutions to the equation $m^2 - n^2 = 88$.
$m^2 - n^2 = 88 = 23(11)$. As in a), we will have have $(m - n) =$
2, $m + n = 44$, Or $(m - n) = 4$, $m + n = 22$. The solution for
$(m - n) = 2$, $m + n = 44$ is $m = 23$, $n = 21$. The solution for
$(m - n) = 4$, $m + n = 22$ is $m = 13$ and $n = 9$
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