Problem 57998. Easy Sequences 111: Repnums as Hypotenuse of Pythagorean Triangles
The number belongs to a class of numbers called Repunit Numbers, in which all digits are 1.
For this problem, we'll define a superset of the repunit numbers which we shall call repnums, which are composed of repeated numbers. That is, if we denote repnums by , then x is the number to be repeated and n is the number of repetitions. Hence, , , and so on.
We can see from the figure below that can be a hypotenuse of a right triangle with integer sides (Pythagorean Triangle).
In fact, this is the only Pythagorean triangle that can be formed with hypotenuse equal to . There is also only one Pythagorean triangle with hypotenuse equal to , that is the triangle with sides , while there are seven Pythagorean triangles with hypotenures of , with legs as follows:
Create the function, , that counts the number of Pythagorean triangles that can be formed with hypotenuse equal to .
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