Solution

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The statement $7^{1734250} \equiv 1660565\pmod{1734251}$ is true. Can you conclude $1734251$ is a composite number?


Yes!

If $1734251$ were prime, then noting that $7 \not\equiv 0\pmod{1734251}$, Fermat's Little Theorem would guarantee that $$7^{1734250} \equiv 1\pmod{1734251}$$ which is clearly not the case.

Thus, $1734251$ is not prime, and instead must be a composite number.