Đáp án:
a^n - b^n = (a-b)[a^(n-1).b + a(n-2).b² +..+ b^(n-1)]
= (a-b).p * 5^2n - 2^n
= 25^n - 2^n = (25-2)p
= 23p
⇒ 5.5^2n - 5.2^n
= 5.23.p
⇒ 5^(2n+1) - 5.2^n = 5.23p ⋮ 23 x 2^(n+4) + 2^(n+1)
= 2^n.2^4 + 2^n.2
= 2^n(2^4 + 2)
= 18.2^n
= 23.2^n - 5.2^n
Vậy: 5^(2n+1) + 2^(n+4) + 2^(n+1)
= 5^(2n+1) - 5.2^n + 23.2^n⋮ 23 ( đpcm )