Oddly Satisfying Numbers

Algebra Level 2

{ P = 201720172017 × 2018201820182018 Q = 201820182018 × 2017201720172017 \begin{cases} P=201720172017 \times 2018201820182018 \\ Q=201820182018 \times 2017201720172017 \end{cases} Find P − Q P-Q .


The answer is 0.

Jason Chrysoprase by Jason Chrysoprase , 18, Indonesia

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1 solution

P − Q = 2017 ( 100010001 ) × 2018 ( 1000100010001 ) − 2017 ( 1000100010001 ) × 2018 ( 100010001 ) = 0 \begin{aligned} P-Q &= 2017(100010001) \times 2018(1000100010001) - 2017(1000100010001) \times 2018(100010001) \\ &=0\\ \end{aligned}

Hence 2017 ( P − Q ) = 2017 ( 0 ) = 0 2017(P-Q) = 2017(0) = \color{#D61F06}{\boxed{0}} .

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