Question

use Euclid division lemma to show that
the any even positive integer is of the form 5m,5m+2,5m+4​

Answer 1

Answer:

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Answer 2

Answer:

hear is your answer

Step-by-step explanation:

Let x be any integer

Then,

Either x=5m or x=5m+1 or x=5m+2 or, x=5m+3 or x=5m+4 for integer x. [ Using division algorithm]

If x=5m

On squaring both side and we get,

x2=25m2=5(5m2)=5n where n=5m2

If x=5m+1

On squaring both side and we get,

x2=(5m+1)2

=25m2+1+10m

=5(5m2+2m)+1(where5m2+2m=n)

=5n+1

If x=5m+2

Then x2

=(5m+2)2

=25m2+20m+4

=5(5m2+4m)+4

=5n+4 [ Taking n=5m2+