Difference between revisions of "AIME 2020(MOCK) Problems"

Revision as of 11:16, 11 June 2020

Problem 1

Let $N$ be $112123123412345... (1000 digits)$ . What is the remainder when $N$ is divided by $21$ ?

Problem 2

Let $K$ be a set of polynomials $P(x)$ with integral coefficients such that the roots of $P(x)$ are $cos \frac{\pi}{7}$ , $cos \frac{\pi}{11}$ , and $cos \frac{\pi}{17}$ . What is the least possible sum of the coefficients of $P(x)$ ?

Problem 3

How many $15$ digit base $5$ positive integers consist of exactly $2$ pairs of consecutive $0$ s but no $4$ consecutive $3$ s?

Problem 4

Let $\lfloor \ x \ rfloor$

@@ Line 13: / Line 13: @@
 How many <math>15</math> digit base <math>5</math> positive integers consist of exactly <math>2</math> pairs of consecutive <math>0</math>s but no <math>4</math> consecutive <math>3</math>s?
+==Problem 4==
+Let <math>\lfloor \ x \ rfloor</math>

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