Question
Question: If number of divisors of a natural number 'n' is 15, the number of solutions (n, m) of n – m<sup>2</...
If number of divisors of a natural number 'n' is 15, the number of solutions (n, m) of n – m2 = 4 (m Ī I) is
A
(a) One
A
(b) Two
C
Zero
D
Infinite
Answer
Zero
Explanation
Solution
Since the number of divisors of 'n' is odd
\ n should be a perfect square
Ž n = t2 (t Ī I)
t2 – m2 = 4 Ž t = 2, m = 0
Ž n = 4 Ž divisors 3
Hence no such number exists