The difference of the square of two natural numbers m and n (m \gt n) is 72. How many pairs of natural numbers will satisfy?

Explanation

We have m^2 - n^2 = (m-n)(m+n) = 72. Since m and n are natural numbers, (m-n) and (m+n) must have the same parity (both even, as their product is even). The even factor pairs of 72 are (2, 36), (4, 18), and (6, 12), which yield 3 valid pairs for (m, n).

Related questions on Arithmetic

• What is the remainder when (17^{25} + 19^{25}) is divided by 18?
• A bottle contains spirit and water in the ratio 1:4 and another identical bottle contains spirit and water in the ratio 4:1. In what rat...
• Let P = 5^5 \times 15^{15} \times 25^{25} \times 35^{35} and Q = 10^{10} \times 20^{20} \times 30^{30} \times 40^{40}. What is the numbe...
• Two students X and Y appeared in a test. The score of X is 20 more than that of Y. If the score of X is 75% of the sum of the scores of X an...
• Question: The product of a natural number N and the number M written by the same digits of N in the reverse order is 252. What is the number...