Question

If a number is divided by 7, the remainder is 4. What will be the remainder when the square of the same
number is divided by 7?
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Answer 1

Step-by-step explanation:

Let the number is n

n = 7k +4 ,

therefore

2n = 7( 2k )+ 8 = 7( 2k + 1 ) + 1 ,

and therefore the remainder is 1.

More interesting would be

When 2n is divided by 7, the remainder is 4. What is the remainder when n is divided by 7?

2n = 7k + 4 ,

therefore

2nn− 4 = 2( n − 2 ) = 7k ,

therefore k is even. Let k=2p , hence

2n = 14p + 4 = 2( 7p + 2 )

or

n = 7p + 2,

therefore the remainder is 2.