Question

show that any positive odd integer is of the form 6q+1, or 6q+3, or 6q+5, where q is some integer

Answer 1

Let a be any positive integer and b = 6
According to Euclid's division algorithm.
a = 6q + r
whereas,
r = 1,2,3,4,5
Now ,
a = 2q
a = 2q + 1
a = 2q + 2
a = 2q + 3
a = 2q + 4
a = 2q + 5
If q is of the form 6q + 1 , 6q +3 , 6q +5 then then q is a odd positive integer ...
( hence proved )

Answer 2

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