self Maths Puzzle

Find the least positive integer d for which there exists an arithmetic progression satisfying the following properties:

Each term of the progression is a positive integer.

The common difference of the progression is d.

No term of the progression appears in the Fibonacci sequence.

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self Other Question

Let S be the number obtained by writing all the numbers from 1 to 100 in order, and removing the spaces in between. Let T be the number obtained by writing all the numbers from 1 to 100 in reverse order and removing the spaces in between.

What is the remainder when T^2−S^2 is divided by 1000? Find the sum of all positive integers n such that 1!×2!×3!×⋯×200!/n! is a perfect square.