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Recent questions tagged number-theory

10 votes
2 answers
32
GATE1991-01,xiii
The number of integer-triples $(i,j,k)$ with $1 \leq i,j,k \leq 300$ such that $i+j+k$ is divisible by 3 is________
The number of integer-triples $(i,j,k)$ with $1 \leq i,j,k \leq 300$ such that $i+j+k$ is divisible by 3 is________
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22 votes
3 answers
35
GATE IT 2007 | Question: 16
The minimum positive integer $p$ such that $3^{p} \pmod {17} = 1$ is $5$ $8$ $12$ $16$
The minimum positive integer $p$ such that $3^{p} \pmod {17} = 1$ is$5$$8$$12$$16$
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14 votes
3 answers
36
GATE IT 2008 | Question: 24
The exponent of $11$ in the prime factorization of $300!$ is $27$ $28$ $29$ $30$
The exponent of $11$ in the prime factorization of $300!$ is$27$$28$$29$$30$
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24 votes
2 answers
38
GATE CSE 2014 Set 3 | Question: GA-10
Consider the equation: $(7526)_8 − (Y)_8 = (4364)_8$, where $(X)_N$ stands for $X$ to the base $N$. Find $Y$. $1634$ $1737$ $3142$ $3162$
Consider the equation: $(7526)_8 − (Y)_8 = (4364)_8$, where $(X)_N$ stands for $X$ to the base $N$. Find $Y$.$1634$$1737$$3142$$3162$
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