What is the last digit of [tex]2222^{50}~+~7777^{16}[/tex]?(adsbygoogle = window.adsbygoogle || []).push({});

I know how to do these kinds of questions, but this time around I decided to try mod 11. Is there a reason why mod 11 does not work in this case?

[tex]2222 \equiv 0~(mod~11)[/tex]

Therefore, [tex]2222^{50} \equiv 0^{50} (mod 11)[/tex], that is

[tex]2222^{50} \equiv 0 (mod 11)[/tex]

I did the same for 7777. [tex]7777^{16} \equiv 0 (mod 11)[/tex]

Thus, I concluded that [tex]2222^{50}~+~7777^{16} \equiv[/tex] 0 + 0 (mod 11). And hence, the last digit is 0.

The last digit is actually 5.

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# Midterm Practice: Find the last digit of a number

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