Can the product of an arithmetic progression of positive integers $n,n+d,\dots ,n+(k-1)d$ of length $k\ge 4$ (with $(n,d)=1$) be a perfect power?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Write the condition “the product is a perfect power” as the Diophantine equation [ n(n+d)\cdots(n+(k-1)d)=y^\ell,\qquad \ell>1, ] with (\gcd(n,d)=1) and (k\ge 4).

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.