Have you heard of Euclidean Algorithm?

(7+7+7++746 times)(29+29+29++2911 times)=3(7+7+7++721 times)(29+29+29++295 times)=2\begin{aligned} (\underbrace{7+7+7+\cdots+7}_{46 \text{ times}}) - (\underbrace{29+29+29+\cdots+29}_{11 \text{ times}}) &= 3 \\\\ (\underbrace{7+7+7+\cdots+7}_{21 \text{ times}}) - (\underbrace{29+29+29+\cdots+29}_{5 \text{ times}}) &= 2 \end{aligned}

Is it also possible to find positive integers mm and nn such that (7+7+7++7m times)(29+29+29++29n times)=1? (\underbrace{7+7+7+\cdots+7}_{m \text{ times}}) - (\underbrace{29+29+29+\cdots+29}_{n \text{ times}}) = 1 ?

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