A Carmichael number is a composite number which satisfies th

A Carmichael number is a composite number which satisfies the conclusion of Fermat\'s Little Theorem. In other words, n is a Carmichael number if whenever a and n are relatively prime then a^n = a (mod n). Show that 561 is a Carmichael number.

Solution

561=3*11*17 is a product of three prime number

lets check the conditions

given condidtions is aⁿ=a (mod n) i.e. aⁿ-a is divisible by n

3⁵⁶¹-3 = is divisible by 561

11⁵⁶¹-11 is also divisible by 561

17⁵⁶¹-17 is also divisible by 561

Hence 561 is carmichael number