Starting with the integer 7^2025, we remove the leftmost digit and add it to the remaining integer.

This process is repeated until the remaining integer has exactly 10 digits. Prove that these ten

digits cannot all be distinct. (Note: It is possible that this "10 digit integer" has a leading digit

equal to 0. You do not need to determine whether or not this is the case, nor do you need to

worry about this in your proof.)