Question

show that the p square will leave a remainder 1 when divided by 8 if P is an odd positive integer

Answer 1

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Answer 2

if p is an odd interger it can be written as 4q+1
p=4q+1
square both sides
p^2= 16q^2 + 8q +1
p^2= 8(2q^2+q) +1
so it leaves remainder 1