A number theory problem by Saumya Gupta
Number Theory
Level
2
P and Q are natural numbers such that P ≥ Q. P + 2Q = 60. Find the number of possibilities for (P, Q).
The answer is 20.
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Till (P, Q) = 20,20 P=Q. This means all the values of Q before 20 will satisfy the Condition that P+2Q = 60 as well as P > Q, i.e, 19 sets of (P, Q). After 20, such as Q= 21 or 22, it will not satisfy P ≥ Q. Thus, there are only 19 + 1 [i.e 1 set of P=Q] will be the sets that follow the conditions as given in the question. Hence, there are 20 possibilities for (P, Q).