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Using euclid's division lemma, show that the square of every positive integer is not of the form 5m+2 or 5m+3 for some integer m.?
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Using euclid's division lemma, show that the square of every positive ...
Let a be any positive integer and b= 5 hence r=0,1,2,3,4. hence we can expand a as bellowa=5q, a=5q+1,a=5q+2 , a=5q+3 , a=5q+4 now a^2=25q^2 =5m. where m= 5q^2, a^2= 25q2+10q+1 a2=5(5q2+2q)+1 = 5m+1, where m= 5q^2+2q a2=25q2+20q+4 =5(5q2+4q)+4 =5m+4 where m= 5q^2+4q a2=25q2+30q+9 =5(5q2+6q)+9 =5m+9. where m= 5q^2+6q a2=25q2+40q+16 =5(5q2+8q)+16 =5m+16. where m= 5q^2+8q we observed that in the expansion of any positive integer is not in the form of 5m+2 or 5m+3
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Using euclid's division lemma, show that the square of every positive integer is not of the form 5m+2 or 5m+3 for some integer m.?
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