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Post New Question
All Questions
+0
237262 Questions
0
22
1
+2729
Number Theory
What is the smallest prime divisor of $5^{19} + 7^{13} + 23$?
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LiIIiam0216
Jul 15, 2024
0
23
1
+2729
Number Theory
How many bases $b \ge 2$ are there such that $100_b + 1_b$ is prime?
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LiIIiam0216
Jul 15, 2024
0
33
1
+1208
Number Theory
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?
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AnswerscorrectIy
Jul 15, 2024
0
23
1
+1208
Number Theory
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?
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AnswerscorrectIy
Jul 15, 2024
0
30
1
+1208
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 $\phi(191)$?
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AnswerscorrectIy
Jul 15, 2024
0
22
1
+1208
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 $\phi(1200)$?
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AnswerscorrectIy
Jul 15, 2024
0
19
0
+2729
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 15, 2024
0
26
0
+2729
Number Theory
Which of the residues $0,$ $1,$ $2,$ $3,$ $4$ satisfy the congruence $3x \equiv 0 \pmod{5}?$
Give your answer as a list, separated by commas, in order from least to greatest.
LiIIiam0216
Jul 15, 2024
0
27
0
+2729
Number Theory
Which of the residues $0,$ $1,$ $2,$ $3,$ $4,$ $5$ satisfy the congruence $x^2 \equiv 0 \pmod{6}?$
Give your answer as a list, separated by commas, in order from least to greatest.
LiIIiam0216
Jul 15, 2024
0
35
1
+2729
Number Theory
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 15, 2024
0
37
0
+2729
Number Theory
Let $a$ be an integer such that $0 \le a \le 10$ and $a^2 \equiv a \pmod{11}$. If $a \neq 0,$ then find the value of $a$.
LiIIiam0216
Jul 15, 2024
0
38
0
+2729
Number Theory
Let $a$ be an integer such that $0 \le a \le 7$ and $a^2 \equiv a \pmod{8}$. If $a \neq 0,$ then find the value of $a$.
LiIIiam0216
Jul 15, 2024
0
12
1
+1208
Number Theory
Find the last two digits of $16*{37}$.
(Compute the remainder when $16*{37}$ is divided by 100.)
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AnswerscorrectIy
Jul 15, 2024
0
33
1
+1208
Number Theory
Find the remainder when $100^{100}$ is divided by $18$.
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AnswerscorrectIy
Jul 15, 2024
0
22
1
+1208
Number Theory
Calculate $40*9 \pmod{23}.$ Express your answer as a non-negative integer that is less than $23$.
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AnswerscorrectIy
Jul 15, 2024
0
25
1
+1208
Number Theory
Find the remainder when $1! + 2! + 3! + \dots + 100!$ is divided by $2$.
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AnswerscorrectIy
Jul 15, 2024
0
28
2
+1208
Number Theory
Given
a &\equiv 1 \pmod{7} \\
b &\equiv 2 \pmod{7} \\
c &\equiv 6 \pmod{7}
read more ..
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AnswerscorrectIy
Jul 15, 2024
0
39
0
+1208
Number Theory
(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 $1^{2^3} = 1^{(2^3)}$.)
AnswerscorrectIy
Jul 15, 2024
0
39
1
+157
Pls help
Mr Ravi spent 1/4 ofhis money on a shirt and 5/6 of his remaining money on a badminton racket, a pair of shorts and 2 pairs of shoes. The badminton racket cost 4 times as much as a pair of shoes while the pair of shorts cost 4 times
read more ..
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sugabreaddoughman
Jul 15, 2024
0
30
2
+157
Help
Watermelons and mangoes are sold at a fruit stall. There were 13 more watermelons than mangoes at first. After 3/5 of the watermelons and 5/9 of the mangoes were sold, there was an equal number of each type of fruit left unsold.
a)
read more ..
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sugabreaddoughman
Jul 15, 2024
0
34
1
+157
Need guide
Baker Yeo sold 120 buns in the morning and 40% of the remaining buns in the afternoon. The number of buns left was 1/3 of the number of buns he had baked. How many buns did he sell in the afternoon?
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sugabreaddoughman
Jul 15, 2024
0
35
1
+157
Help
In a fruit stall, there were 119 more apples than oranges. 6/7 of the apples and 4/5 of the oranges were sold. As a result, there were 33 more oranges than apples left.
(a) How many oranges were there at first?
(b)
read more ..
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sugabreaddoughman
Jul 15, 2024
0
28
1
+1208
Number Theory
(a) Find the last two digits of $9*7*8$.
(b) Find the last two digits of $2^{3^4}$. (By convention, exponent towers are evaluated from the top down, so $2^{3^4} = 2^{(3^4)}$.)
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AnswerscorrectIy
Jul 15, 2024
0
19
1
+1208
Number Theory
(a) Find the last two digits of $9*7*11$.
(b) Find the last two digits of $4^{5^6}$. (By convention, exponent towers are evaluated from the top down, so $4^{5^6} = 4^{(5^6)}$.)
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AnswerscorrectIy
Jul 15, 2024
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