binomial theorm

prove that
[ (8+3âˆš7)²⁰ ] is odd
[] is gif

2 Answers

Let (8+3√7)²⁰ = I+f where I =[(8+3√7)²⁰ ] and 0<f<1

now (8-3√7)²⁰ =d

we find that 0,<8-3√7<1
=> 0<d<1

now
I+f+d= (8+3√7)²⁰+(8-3√7)²⁰
=> I+f+d= 2K (where k=integer)
=> f+d= integer

also 0<f+d<2
=>f+d=1

=>I=2k-1

thus I is odd.
[(8+3√7)²⁰] is odd

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