## Euclid 2022 Question 2, CEMC UWaterloo

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#### Difficulty: 5

#### This problem is tagged with euclid, euclid22, highschool.

**(Euclid 2022, Question 2, CEMC - UWaterloo)**

(a) Find the three ordered pairs of integers $(a, b)$ with $1 < a < b$ and $ab = 2022$.

(b) Suppose that $c$ and $d$ are integers with $c > 0$ and $d > 0$ and $\frac{2c + 1}{2d + 1}=\frac{1}{17}$. What is the smallest possible value of $d$?

(c) Suppose that $p$, $r$ and $t$ are real numbers for which $(px + r)(x + 5) = x^2 + 3x + t$ is true for all real numbers $x$. Determine the value of $t$.

*Answer Submission Note(s)*

In part (a), format each pair as (a,b) and sort them in increasing values of a, then separate them with a comma.

Separate the answers for each part with a single space.

The correct format looks like: "(a1,b1),(a2,b2),(a3,b3) d t"

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