The familiar Pythagorean 3-4-5 triple gives one solution to (x-1)^n
+ x^n = (x+1)^n so what about other solutions for x an integer and
n= 2, 3, 4 or 5?
A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?
If the last four digits of my phone number are placed in front of the remaining three you get one more than twice my number! What is it?
Take a cue from the title!
Can you in any way use $a$, $b$ and $c$ where you know $a^2 + b^2 = c^2$?
No knowledge is needed here, only mathematical reasoning. It is an important point to make that finding a method for producing solutions does not prove that there is no other method and no smaller solution generated another way. However, once you have found what you believe to be the smallest solution, it is possible to check numerically that there are in fact no smaller solutions.