If a and b are two odd positive integers such that a is greater than b ,then prove that one of the two numbers a+b÷2 and a-b÷2 is odd and the other is even.
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We know that any odd +ve int. is of the form 4q+1 or 4q+3.
Let a=4q+3, b=4q+1. [a>b]
a+b/2= 8q+4/2=4q+2.........(even)
a-b/2=4q+3-4q-1/2=2/2=1..........(odd)
Let a=4q+3, b=4q+1. [a>b]
a+b/2= 8q+4/2=4q+2.........(even)
a-b/2=4q+3-4q-1/2=2/2=1..........(odd)
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