Remainders!!

Algebra Level 2

What is the remainder when ∏ n = 3 33 ∣ 2 n 4 − 25 n 3 + 33 n 2 ∣ \displaystyle \prod _{n=3}^{33} \left|2n^4 - 25n^3 +33n^2 \right| is divided by 2019?


The answer is 0.

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

We can write 2 n 4 − 25 n 3 + 33 n 2 2n^4-25n^3+33n^2 as n 2 ( n − 11 ) ( 2 n − 3 ) n^2(n-11)(2n-3) which equals zero at n = 11 n=11 . So the product is zero, and the required remainder is also zero.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Totally True.

Hana Wehbi - 1 year, 7 months ago

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