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SASMO 2021 Grade 9 Question 23

SASMO · SASMO 2021 Grade 9

Question 23

A triangle has positive integer side lengths $m,n,150$. The difference between two of its side lengths is 26. The last two digits of $m^2$ and $n^2$ are identical, and $m>n$. Find the smallest possible $m$.

Answer format: an integer without units. Leading zeros are optional; the source uses four digit boxes.