Question

Let p > 5 be the prime number. Prove that the expression p^4– 10p^2 + 9 is divisible by 1920.

Answer 1

Answer:

Let us take few examples before we prove the required result.Let us take few examples before we prove the required result.

Letp=2Letp=2

(p−1)(2p−1)=(2−1)(4−1)=(1)(3)=3(p−1)(2p−1)=(2−1)(4−1)=(1)(3)=3

6∤36∤3

Letp=3Letp=3

(p−1)(2p−1)=(3−1)(6−1)=(2)(5)=10(p−1)(2p−1)=(3−1)(6−1)=(2)(5)=10

6∤106∤10

That is why a condition has been imposed that p is a prime number≥5That is why a condition has been imposed that p is a prime number≥5

Letp=5Letp=5

(p−1)(2p−1)=(5−1)(10−1)=(4)(9)=36(p−1)(2p−1)=(5−1)(10−1)=(4)(9)=36

6∣366∣36

Letp=7Letp=7

(p−1)(2p−1)=(7−1)(14−1)=(6)(13)=78(p−1)(2p−1)=(7−1)(14−1)=(6)(13)=78

6∣786∣78

We need to prove that for a prime p≥5(p - 1)(2p - 1) is alwaysWe need to prove that for a prime p≥5(p - 1)(2p - 1) is always

Step-by-step explanation:

it's ur ans..

HOPE IT'S HELPFUL..