MEMEG0D

65 Questions
3 Answers

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Number Theory

Find the greatest prime divisor of the value of the arithmetic series
1 + 2 + 3 + \dots + 135 + 136 + 137 + 138 + 139 + 140.

MEMEG0D vor 2 Stunden

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Number Theory

When fractions are expressed in different bases, they can be terminating or repeating. For example, when \frac{1}{5} is expressed in base 3, the result is
0.\overline{0121}_3 = 0.01210121 \dots,
which is repeating.
When mehr ..

MEMEG0D vor 2 Stunden

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Counting

Find the number of ways that Magnus can give out $12$ identical stickers to $2$ of his friends, if every friend gets at least one sticker.

MEMEG0D 04.11.2024

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Counting

Miyu is giving out $8$ identical chocolates to her $5$ friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets exactly $7$ chocolates?

MEMEG0D 04.11.2024

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2

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Counting

How many solutions are there to the equation
u + v + w + x + y + z = 2,
where $u,$ $v,$ $w,$ $x,$ $y,$ and $z$ are nonnegative integers, and $x$ is at most $1?$

MEMEG0D 04.11.2024

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2

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Number Theory

Carl writes eight consecutive three-digit numbers on a blackboard. Each number that Carl writes is divisible by 2, 3, 4, or 5. What is the sum of the digits of the smallest number that Carl wrote?

MEMEG0D 30.10.2024

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2

2

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Number Theory

When a prime is divided by 60, the remainder is a composite number. When a second prime is divided by 60, the remainder is a prime. Find the smallest possible value of the second prime.

MEMEG0D 30.10.2024

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3

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Number Theory

How many three-digit numbers are equal to five times the sum of their digits?

MEMEG0D 30.10.2024

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3

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Number Theory

A four-digit hexadecimal integer is written on a napkin such that the units digit is illegible. The first three digits are 2, $F$, and 1. If the integer is a multiple of $19_{10}$, what is the units digit?

MEMEG0D 29.10.2024

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2

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Number Theory

The numbers $24^2 = 576$ and $56^2 = 3136$ are examples of perfect squares that have a units digits of $6.$
If the units digit of a perfect square is $5,$ then what are the possible values of the tens digit?

MEMEG0D 29.10.2024

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4

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+260

Number Theory

Which of the residues 0, 1, 2, ..., 11 satisfy the congruence 3x = 1 mod 12?

MEMEG0D 29.10.2024

0

4

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+260

Number Theory

Which of the residues 0, 1, 2, 3, 4 satisfy the congruence x^5 = 0 mod 5?

MEMEG0D 29.10.2024

+1

6

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+260

Number Theory

What are the first 5 digits after the decimal point (technically the hexadecimal point...) when the fraction $\frac{2}{7}$ is written in base $16$?

MEMEG0D 28.10.2024

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5

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Number Theory

Let $N$ be a positive integer. The number $N$ has three digits when expressed in base $7$. When the number $N$ is expressed in base $12$, it has the same three digits, in reverse order. What is $N$? (Express your answer in decim mehr ..

MEMEG0D 28.10.2024

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4

0

+260

Number Theory

What is the largest positive integer $n$ such that $1457$, $1797$, $709$, $15$, $24$, $197$, $428$ all leave the same remainder when divided by $n$?

MEMEG0D 28.10.2024

+260

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The answer is 19.

MEMEG0Dvor 1 Stunde