The largest integer p for which p+10 divides p^{3}+100

simsek6li

simsek6li

Answered question

2022-02-04

The largest integer p for which p+10 divides p3+100

Answer & Explanation

Ashly Forbes

Ashly Forbes

Beginner2022-02-05Added 12 answers

Step 1
This is an interesting question.
p3+100=(p+10)(p210p+100)900
So if p+10 is a divisor of p3+100, then it must also be a divisor of 900
The largest integer divisor of 900 is 900, yielding p=890

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