Question

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Answer 1

Answer:

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Step-by-step explanation:

By Euclid's division lemma,

a=bq+r, 0≤r<b

Let a be any integer

b-3

Any integer can be 3q, 3q+1, 3q+2

CaseI-3q

Square- 9q^2=3m

CaseII-3q+1

Square-9q^2+1+6q

=3m+1

CaseIII-3q+2

Square-9q^2+4+12q

=3m+1

Hence any square integer can only be 3q or 3q+1

Hence proved

Answer 2

By Euclid's division lemma,

a=bq+r, 0≤r<b

Let a be any integer

b-3

Any integer can be 3q, 3q+1, 3q+2

CaseI-3q

Square- 9q^2=3m

CaseII-3q+1

Square-9q^2+1+6q

=3m+1

CaseIII-3q+2

Square-9q^2+4+12q

=3m+1

Hence any square integer can only be 3q or 3q+1