Question

Show that..... n square + n+1 is not divisible by 5 for any n where n is a natural number

Answer 1

Answer:

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Answer 2

Your answer is given below =》》》

Any natural number it's "

n = 5k

n = 5k±1

n = 5k±2

where k natural number k

Case n = 5k then

n^2+n+1 = 25k^2+5k+1 = 5k(k+1)+1 then not divisible by 5 (remainder 1)

CAse n = 5k±1 then

n^2+n+1 = 25k^2 ± 10k+1 + 5k±1+1 = 5k(5k±1) +2±1 then not divisible by 5 (remainder 3 or 1)

CAse n = 5k±2

n^2+n+1 = 25k^2 ± 10k+4 + 5k±2+1 = 5k(5k±1+1) ± 2 then not divisible by 5 (remainder 2 or 3)

Then

n^2+n+1 not divisible by 5