By using "Ecuclids division lemma" show that the squre of any positive integer
is of the form 5p, 5p + 1,5p + 4
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Step-by-step explanation:
By euclid division lemma,
a=bq+r,0<and=r<b
a=5q+r,0<and=r<5
Possible nos. are a=5q,5q+1,5q+2,5q+3,5q+4
a^2=25q^2........(squaring)
a^2=5(5q^2)
a^2=5p........i)
Similarly we can prove a^2=5p+1,5p+4
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