Remainder

Number Theory Level 2

Find the remainder when $2^{55}$ is divided by 7.

1 3 4 0 5 6 2

1 solution

Rindell Mabunga
Aug 1, 2015

Remember that

$2^3 = 1(mod 7)$

Since

$2^{55} = 2^{54} \times 2 = (2^3)^{18} \times 2$

Then

$2^{55}(mod 7) = (2^3)^{18} \times 2 (mod 7) = 1^{18} \times 2 (mod 7) = 1 \times 2 (mod 7) = 2 (mod 7)$

Nice solution. Just did it in the mind . But note that it is $\equiv$ not $=$ .

Chirayu Bhardwaj - 5 years, 2 months ago

I did the same, too. :)

By the way, use \equiv to enter $\equiv$ . Also, enclose the text in \mathrm{ ... } to make it unitalicized, so for example, \mathrm{mod} becomes $\mathrm{mod}$ .

Jaydee Lucero - 4 years, 11 months ago

Remainder

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