Problem:
Question:
How did the author derive $$gcd(p-1,d)=1$$? how it is true?
Reference:
- Page 33 of An Introduction to Diophantine Equations by Titu Andreescu, Dorin Andrica, Ion Cucurezeanu
2026-03-25 22:10:10.1774476610
Greatest Common Divisor in a Diophantine Equation
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$p$ is the least prime factor of $d$. So $p-1$ contains no prime factor of $d$... (if it did $p$ wouldn't be the least such). Since $p-1$ and $d$ have no prime factor in common, they are coprime.