Find the smallest value of $a\in\mathbb{N}$ such that $7^{21}\cdot 2^{50}+a$ divisible by $9$.
The only thing I know is that an integer is divisible by $9$ is the sum of its digits is divisible by $9$.
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Do you know the phi function – Aditya Dwivedi Mar 04 '21 at 11:52
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What is the relationship between $a$ and $k,$? – John Bentin Mar 04 '21 at 11:54
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I know something, but not too much. – stefano Mar 04 '21 at 11:55
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@John Bentin My fault, I made some changes. – stefano Mar 04 '21 at 11:56
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2Hint: $\bmod 9!:\ 7\equiv -2,$ and $,2^3\equiv -1,$ so $,2^6\equiv 1\ \ $ – Bill Dubuque Mar 04 '21 at 12:08