Find the last digit of the number 77^7. (The powers are calculated from the top down: 77^7 = 7^(7^7))
A number made of several sevens was written on the board: 777...77. Vlad erased the last digit of this number, multiplied the remaining part by 3, and added the erased digit back. He repeated this operation several times. Prove that eventually he will get the number
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