Question

neN is a2(a+1)n+1-na-(a+1),aEN prove

Answer 1

Let a be 2

If 1 + a + a² + a³ + an = (1 + a) (1 + a²) (1 + a⁴)

then 1 + 2 + 4 + 8 + 2n = (1+2)(1+4)+(1 + 16)

so,

15 + 2n = (3)(5)(17)

15 + 2n = 15*17

15 + 2n = 255

2n = 255 - 15

2n = 240

n = 240/2

n = 120

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