Question

State true or false for each of the following statements and justify in each case :

n² – 1 is divisible by 8, if n is

State the "Fundamental Theorem of Arithmetic" and use it to find LCM of 36 and 54.

Show that 45ⁿ can not end with the digit 0, n being a natural number. Write the prime number 'a' which on multiplying with 45ⁿ makes the product end with the digit 0.

Assertion (A): Every positive even integer is a multiple of 2. Reason (R): The Fundamental Theorem of Arithmetic ensures the unique prime factorization of integers greater than 1.