Love ❤ for Pythagoras!
Let the probability for a random natural number under 10 being absent in any of Pythagorean triplets under 10 (inclusive) be 'p'
Let the probability for a random natural number under 100 being absent in any of Pythagorean triplets under 100 (inclusive) be 'q'
What is ?
BONUS: 1) What is the probability of a natural multiple of 5 being absent in any Pythagorean Triplet? And why?
2) What is the probablity of a natural number being absent in a Pythagorean Triplet under 1000 and 10000?
The answer is 0.0169.
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1 solution
Mathematica
N[((10-#)/10-(100-#2)/100)^2&@@(Length@Union@Flatten[{a, b, c}/.Solve[a^2+b^2==c^2&&0<a<b<c<=#,{a,b,c},Integers]]&/@{10,100})]0.0169
using the same code we can find the probability for:
1000 -> 41/200
10000 -> 1669/10000