Question

n =2p-3,p ∈ N and divide n² by 4 what will be the remainder?​

Answer 1

Given :   n =2p-3,  p ∈ N    ,

To Find : remainder if divide n² by 4

Solution:

 n =2p-3,

Squaring both sides

=> n² = (2p - 3)²

=> n² = (2p)²  - 2(2p)3 + 3²

=> n² = 4p²  - 4p(3)  + 9

=> n² = 4.p² - 4.3p  +  8 + 1

=> n² = 4(p²  - 3p  + 2 )  + 1

=> n² = 4k + 1

if divide n² by 4  then remainder =  1  

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