Question

When x200 + 1 is divided by x2 + 1, the remainder is equal to

Answer 1

Answer:

when x²⁰⁰ + 1 is divided by x² + 1  the reminder = 2

Step-by-step explanation:

When x200 + 1 is divided by x2 + 1, the remainder is equal to

x²⁰⁰ + 1 =  x²⁰⁰ + (x¹⁹⁸ - x¹⁹⁸ - x¹⁹⁶ + x¹⁹⁶ + x¹⁹⁴  - x¹⁹⁴ - x¹⁹² + x¹⁹² +x¹⁹⁰ - x¹⁹⁰ +..................-x⁴ + x⁴ + x² - x² - 1 + 1 )+ 1

=> x²⁰⁰ + 1  = x²⁰⁰ + x¹⁹⁸ - x¹⁹⁸ - x¹⁹⁶ + x¹⁹⁶ + x¹⁹⁴  - x¹⁹⁴ - x¹⁹² + x¹⁹² +x¹⁹⁰ - x¹⁹⁰ +..................-x⁴ + x⁴ + x² - x² - 1 + 1 + 1

=> x²⁰⁰ + 1  = x¹⁹⁸(x² + 1) - x¹⁹⁶(x² + 1) + x¹⁹⁴(x² + 1)  - x¹⁹²(x² +1) + x¹⁹⁰(x² +1) - x¹⁸⁸(x²+1) +..................+ x²(x² + 1) - (x² + 1) + 1 + 1

=>  x²⁰⁰ + 1  = x¹⁹⁸(x² + 1) - x¹⁹⁶(x² + 1) + x¹⁹⁴(x² + 1)  - x¹⁹²(x² +1) + x¹⁹⁰(x² +1) - x¹⁸⁸(x²+1) +..................+ x²(x² + 1) - 1.(x² + 1) + 2

=>  x²⁰⁰ + 1  = (x² + 1)(x¹⁹⁸- x¹⁹⁶ + x¹⁹⁴ - x¹⁹² + x¹⁹⁰ - x¹⁸⁸+..................+ x² - 1) + 2

=> when x²⁰⁰ + 1 is divided by x² + 1  the reminder = 2