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Euler problems/131 to 140

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Contents

1 Problem 131

Determining primes, p, for which n3 + n2p is a perfect cube.

Solution:

2 Problem 132

Determining the first forty prime factors of a very large repunit.

Solution:

3 Problem 133

Investigating which primes will never divide a repunit containing 10n digits.

Solution:

4 Problem 134

Finding the smallest positive integer related to any pair of consecutive primes.

Solution:

5 Problem 135

Determining the number of solutions of the equation x2 − y2 − z2 = n.

Solution:

6 Problem 136

Discover when the equation x2 − y2 − z2 = n has a unique solution.

Solution:

7 Problem 137

Determining the value of infinite polynomial series for which the coefficients are Fibonacci numbers.

Solution:

8 Problem 138

Investigating isosceles triangle for which the height and base length differ by one.

Solution:

9 Problem 139

Finding Pythagorean triangles which allow the square on the hypotenuse square to be tiled.

Solution:

10 Problem 140

Investigating the value of infinite polynomial series for which the coefficients are a linear second order recurrence relation.

Solution: