## Euclid 2023 Question 3, CEMC UWaterloo

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#### Difficulty: 6

#### This problem is tagged with euclid, euclid23, highschool.

**(Euclid 2023, Question 3, CEMC - UWaterloo)**

(a) The positive divisors of $6$ are $1$, $2$, $3$, and $6$. What is the sum of the positive divisors of $64$?

(b) Fionn wrote $4$ consecutive integers on a whiteboard. Lexi came along and erased one of the integers. Fionn noticed that the sum of the remaining integers was $847$. What integer did Lexi erase?

(c) An arithmetic sequence with $7$ terms has first term $d^2$ and common difference $d$. The sum of the $7$ terms in the sequence is $756$. Determine all possible values of $d$.

(An *arithmetic sequence* is a sequence in which each term after the first is obtained from the previous term by adding a constant, called the common difference. For example, $3$, $5$, $7$, $9$ are the first four terms of an arithmetic sequence.)

*Answer Submission Note(s)*

In part (c), sort your answers in ascending order and separate them with a comma.

Separate the answers for each part with a single space.

For example: "a b c1,c2"

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