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anonymous
 5 years ago
Suppose that a is an integer number. Show that if a^2 is divisble by 5, then a is divisble by 5. Hint: A integer divisble by 5 if its last digit is either 0 or 5..
By contraposition: Let k be an integer that is not divisible by 5.
⟹k=5q+r, such that q∈Z and r∈{1,2,3,4}
⟹k2=(5q+r)2=25q2+10qr+r2=5(5q2+2qr)+r2
⟹k2 is not divisable by 5. QED.
Noww..
anonymous
 5 years ago
Suppose that a is an integer number. Show that if a^2 is divisble by 5, then a is divisble by 5. Hint: A integer divisble by 5 if its last digit is either 0 or 5.. By contraposition: Let k be an integer that is not divisible by 5. ⟹k=5q+r, such that q∈Z and r∈{1,2,3,4} ⟹k2=(5q+r)2=25q2+10qr+r2=5(5q2+2qr)+r2 ⟹k2 is not divisable by 5. QED. Noww..

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