Question

Q. The number of ordered triplets (x,y,z) such that x,y and z are primes and x^y + 1= z is

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Answer 1

The number of ordered triplets (x, y, z) such that x, y, and z are primes and x^ y + 1= z is one, which is (2,2,5).

• When z is an even number, the sole answer is z=2 or $x^y$ =1. There is no answer because this is only feasible if x=1 or y=0.
• When z is odd $x^y$ must be even, hence x must also be even, implying that x=2. However, according to this post, if $2^y$ +1 is prime, y must be a power of two. The only y that meets this requirement is 2, hence (2,2,5) is the sole option.
• Thus, the number of ordered triplets such that x, y, and z are prime numbers and the given equation is satisfied is only one.

Answer 2

Answer:

1 is the answer of this ....