MathDB

1

Part of 2016 Argentina National Olympiad

Problems(1)

arithmetic progression of 2016 terms whose product is perfect power

Source: 2016 Argentina OMA Finals L3 p1

1/16/2023
Find an arithmetic progression of 20162016 natural numbers such that neither is a perfect power but its multiplication is a perfect power.
Clarification: A perfect power is a number of the form nkn^k where nn and kk are both natural numbers greater than or equal to 22.
number theoryPerfect powerarithmetic sequence