Binary difference

Number Theory Level 2

Is 10101 0 4 − 10101 0 2 101010_4 - 101010_2 divisible by 4?

No Yes

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

Chew-Seong Cheong
Feb 13, 2018

10101 0 4 − 10101 0 2 ≡ ( 4 5 + 4 3 + 4 1 − 2 5 − 2 3 − 2 1 ) 10 (mod 4) ≡ 0 + 0 + 0 − 0 − 0 − 2 (mod 4) ≡ − 2 (mod 4) ≡ 2 (mod 4) \begin{aligned} 101010_4 - 101010_2 & \equiv (4^5+4^3+4^1-2^5-2^3-2^1)_{10} \text{ (mod 4)} \\ & \equiv 0+0+0-0-0-2 \text{ (mod 4)} \\ & \equiv - 2 \text{ (mod 4)} \\ & \equiv 2 \text{ (mod 4)} \end{aligned}

No , 10101 0 4 − 10101 0 2 101010_4 - 101010_2 is not divisible by 4.

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Which actually holds for every number of this form.

Peter van der Linden - 3 years, 3 months ago

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