Two number and are randomly chosen from the set of natural numbers. Then, the probability that the value of is non-zero, equals

Question

Two number  and  are randomly chosen from the set of natural numbers. Then, the probability that the value of  is non-zero, equals

Canvas Classes · Accepted Answer

🧠 The Cycle of  — Reduce to

Read the question slowly. We have two natural numbers , and we want the probability that .

Notice the key fact about : its powers cycle through four values.
- , and then it repeats.

So  depends ONLY on . The remainder when  is divided by  is uniformly  or  — each with probability . This is the picture: there are effectively only  "types" of  pairs, all equally likely.

This is the trick I want you to remember. When a problem mentions  with  "random", forget the a

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