Prove that when a positive odd integer p is divided by 8 we get remainder 1
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We can solve this by trial and error method. Or,
As we know when we multiply a number with any one of its multiples we will get a quotient without a remainder.
For example: 40/8=5.
Hence, to get a remainder one we can just add one to any one of its multiple.
For example: 40+1 =41.
41/8 will give us quotient as 5 and remainder as 1.
If we take another multiple of 8 say, 16 or 24 or 32 and add one with each we still will get a remainder one.
That is: 17/8= remainder one.
25/8=remainder one.
33/8=remainder one.
As we know when we multiply a number with any one of its multiples we will get a quotient without a remainder.
For example: 40/8=5.
Hence, to get a remainder one we can just add one to any one of its multiple.
For example: 40+1 =41.
41/8 will give us quotient as 5 and remainder as 1.
If we take another multiple of 8 say, 16 or 24 or 32 and add one with each we still will get a remainder one.
That is: 17/8= remainder one.
25/8=remainder one.
33/8=remainder one.
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