Project Euler Forum

Problem 94 uses the word "integral" when it should read "integer," as in "integral length sides" instead of "integer length sides"

That's standard terminology. Integer is the noun, integral the adjective.

DJohn is right, but sometimes common usage makes what is best practice obsolete.

Warning: Potentially boring grammar lesson ahead...

An adjective is used to modify or add an attribute to a noun (name of a thing). For example, when you have tasty food, the word "tasty" is used to add a quality (tastiness) to the food.

As DJohn explained, the word "integral" is the adjectival form of the noun "integer". So in the case of the wording used in this problem the adjective "integral" adds a quality to the noun, "length". However, sometimes a noun can operate as an adjective or modifier. This is called a noun adjunct or attributive noun.

In the food example above you could say, "dog food". Dog is a noun, but operates as a modifier to the noun "food" and is adding a quality/attribute to it. Similarly, you can say integer length, and here the noun "integer" operates as an attributive noun.

Technically when an adjectival form exists it is preferred, but grammatical "rules" mean nothing when more people tend to say integer length than integral length.

Perhaps it's good to add that "integral" can also be a noun.
E.g the concept of an integral in Calculus (an antiderivative used to calculate an area and other uses) .
However, in the wording of problem 94 'integral' is an adjective.