self Maths Puzzle

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?

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self Other Question
n is a two digit number such that n^2 is a four digit number with the first 2 digits equal to each other and the last 2 digits equal to each other. What is the value of n? 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.