Question

When a number is divided by 5, the remainder is 3. What will be the remainder when sum of cube of that number and square of that number is divided by 5?

Answer 1

Answer:

let x be the number

given

number is divided by 5, the remainder is 3

x = 5k +3

now             x^3 +x^2 = x^2[x + 1]  

                                      = [5k +3]^2  [5k +4]  

                                      =  5[N] + 3^2 [4]   here N is an integer

                                       = 5N +36

                                          =5N +35 +1

                                          =5[N+7] +1

                                            = multiple of 5     + 1  

1 will be the remainder when sum of cube of that number and square of that number is divided by 5