Question 966372
1.{{{X/237=M+112}}}
2.{{{Y/117=N+108}}}
3.{{{X/237=Y/117}}}
where {{{M}}}, {{{N}}} are integers.
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From eq. 1,
{{{X/237=M+112}}}
{{{X=237M+26544}}}
From eq. 2,
{{{Y=17N+12636}}}
From eq. 3,
{{{M+112=N+108}}}
{{{M=N-4}}}
{{{N=M+4}}}
Then the sum becomes,
{{{(X+Y)/118=(237M+26544+117N+12636)/118}}}
{{{(X+Y)/118=(237M+26544+117(M+4)+12636)/118}}}
{{{(X+Y)/118=(237M+26544+117M+468+12636)/118}}}
{{{(X+Y)/118=(354M+39648)/118}}}
{{{(X+Y)/118=(354M/118)+(39648/118)}}}
{{{(X+Y)/118=3M+336}}}
The remainder is zero.