Question

If M= 19^3 + 21^3 +23^3+25^3, then what will be the remainder if M is divided by 44?​

Answer 1

If M= 19^3 + 21^3 +23^3+25^3, then what will be the remainder if M is divided by 44?

Good question,

Here is your perfect answer!

M = 19^3 + 21^3 +23^3+25^3

= (19³ + 25³) + (23³ + 21³)

= (19+25) (19²+25²-19.25) + (23+21) (23² + 21² - 23.21)

= 44(19²+25²-19.25) + 44(23² + 21² - 23.21)

To find remainder when divided by 44,

= 44(19²+25²-19.25) + 44(23² + 21² - 23.21) /44

= 44(19²+25²-19.25)/44 + 44(23² + 21² - 23.21) /44

Hence remainder = 0, as you can see :)

Answer 2

M = 19^3 + 21^3 + 23*23*23 + 25^3

M = 19^3 + (19+2)^3 + (19+4)^3 + (19+6)^3

M = 43912

hence, M/44 = 43912/44 = 998

Hence. Remainder is 0