Pandigital Squares
September 29, 2020
A pandigital number, like 4730825961, is a ten-digit number in which each digit from zero to nine appears exactly once. A square number, like 25² = 625, is a number with an integral square root.
Your task is to write a program that finds all of the pandigital square numbers. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.
8424432925592889329288197322308900672459420460792433
September 1, 2020
Regular readers know of my affinity for number theory. Today’s exercise is a reflection of that.
It is conjectured that the two numbers produced by the equations n17 + 9 and (n + 1)17 + 9 for a given n are always co-prime (that is, their greatest common divisor is 1). Is that conjecture correct?
Your task is to either prove that the greatest common divisor is always 1 or write a program that finds a case where the greatest common divisor is not 1. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.
Programming Praxis 