All Questions ⁺⁰236009 Questions

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help me quick

Compute
4 + \cfrac{1}{4 + \cfrac{1}{4 + \cfrac{1}{4}}}}

LiIIiam0216 Jul 27, 2024

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need help

Write the following expression as a fraction in lowest terms:
2 + \cfrac{3}{3 + \cfrac{3}{3 + 3}}.

LiIIiam0216 Jul 27, 2024

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help help

How many lattice points (points with integer coordinates) are on the line segment whose endpoints are $(3,17)$ and $(82,150)?$ (Include both endpoints in your count.)

LiIIiam0216 Jul 27, 2024

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10

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+355

Let m and n be non-negative integers. If m=6n+2, then what integer between 0 and m is the inverse of 3 modulo m? Answer in terms of n.

Let m and n be non-negative integers. If m=6n+2, then what integer between 0 and m is the inverse of 3 modulo m? Answer in terms of n.

Lilliam0216 Jul 27, 2024

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need help

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 read more ..

LiIIiam0216 Jul 27, 2024

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10

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help mods

Find the smallest positive integer $N$ such that
N &\equiv 2 \pmod{3}, \\
N &\equiv 2 \pmod{7}, \\
N &\equiv 2 \pmod{10}.

LiIIiam0216 Jul 27, 2024

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15

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+2653

help with mods

Find the smallest positive integer $N$ such that
N &\equiv 2 \pmod{5}, \\
N &\equiv 2 \pmod{7}.

LiIIiam0216 Jul 27, 2024

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help me

(a) Find the last two digits of $9*5*3$.
(b) Find the last two digits of $1^{2^3}$. (By convention, exponent towers are evaluated from the top down, so $1^{2^3} = 1^{(2^3)}$.)

LiIIiam0216 Jul 27, 2024

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8

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i need help

Given
a &\equiv 1 \pmod{7} \\
b &\equiv 2 \pmod{7} \\
c &\equiv 6 \pmod{7} read more ..

LiIIiam0216 Jul 27, 2024

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help help

Find the remainder when $1! + 2! + 3! + \dots + 100!$ is divided by $2$.

LiIIiam0216 Jul 27, 2024

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19

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need help

Let $a$ be an integer such that $a \equiv 5 \pmod{7}$. Find the value of $a + 1 \pmod{7}$. Express your answer as a residue between $0$ and the modulus.

LiIIiam0216 Jul 27, 2024

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Number Theory

Which of the residues $0,$ $1,$ $2,$ $\dots,$ $11$ satisfy the congruence $3x \equiv 8 \pmod{5}?$
Give your answer as a list, separated by commas, in order from least to greatest.

LiIIiam0216 Jul 27, 2024

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18

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help number theory

For a positive integer $n$, $\phi(n)$ denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$.
What is $\phi(191)$?

LiIIiam0216 Jul 27, 2024

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9

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+2653

help me help

The number $100$ has four perfect square divisors, namely $1,$ $4,$ $25,$ and $100.$
What is the smallest positive integer that has exactly $2$ perfect square divisors?

LiIIiam0216 Jul 27, 2024

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need help

A terminal zero is a $0$ that appears at the end of a number. For example, the number $3,800$ has two terminal zeros.
How many terminal zeroes does $40 \cdot 6 \cdot 75 \cdot 12$ have?

LiIIiam0216 Jul 27, 2024

Jul 26, 2024

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help 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 $16$?

LiIIiam0216 Jul 26, 2024

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need help

On planet Enigma, the residents use a currency called the confusion. There are only two confusion bills on Enigma, one worth $7$ confusions and the other worth $12$ confusions. There are also some coins of smaller value, but each weighs over read more ..

LiIIiam0216 Jul 26, 2024

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I have been trying to do my homework all day and i need help please and thank you

The position of a particle is given by the parametric equations
as t ranges over all real numbers.

x=3+2sin(2t)
y=4+2cos(2t)
The particle visits the points P, Q, R, S at times -pi/6, 0, pi/3, pi/2 in some order. Order read more ..

JRFPLSHelp Jul 26, 2024

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14

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+893

Number Theory

Given
a &\equiv 1 \pmod{7} \\
b &\equiv 2 \pmod{7} \\
c &\equiv 6 \pmod{7} read more ..

AnswerscorrectIy Jul 26, 2024

0

8

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+893

Number Theory

Find the remainder when $1! + 2! + 3! + \dots + 100!$ is divided by $2$.

AnswerscorrectIy Jul 26, 2024

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18

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+893

Number Theory

For a certain positive integer $n$, the number $n^{6873}$ leaves a remainder of $3$ when divided by $23.$ What remainder does $n$ leave when divided by $23$?

AnswerscorrectIy Jul 26, 2024

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Number Theory

For an integer $n,$ let $f(n)$ be the remainder when $n^8 + n^{16}$ is divided by $5.$ Compute $f(0) + f(1) + f(2) + f(3) + f(4).$

AnswerscorrectIy Jul 26, 2024

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help with mods

Find the last three digits of $35*{781}$.

LiIIiam0216 Jul 26, 2024

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