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Omni-MATH / Let k be a fixed even positive integer, N is the product of k distinct primes p₁,...,p_(k), a,b are two positive integers, a,b≤N. Denote S₁={d| d|N,a≤d≤b,d has even number of prime…

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problem

Let kk be a fixed even positive integer, NN is the product of kk distinct primes p1,...,pkp_1,...,p_k, a,ba,b are two positive integers, a,b≤Na,b\leq N. Denote S1={d|S_1=\{d| d|N,a≤d≤b,dd|N, a\leq d\leq b, d has even number of prime factors}\}, S2={d|S_2=\{d| d|N,a≤d≤b,dd|N, a\leq d\leq b, d has odd number of prime factors}\}, Prove: |S1|−|S2|≤Ckk2|S_1|-|S_2|\leq C^{\frac{k}{2}}_k
Plain-text mathematical notation (without MathML)
Let k be a fixed even positive integer, N is the product of k distinct primes p₁,...,p_(k), a,b are two positive integers, a,b≤N. Denote 
S₁={d| d|N,a≤d≤b,d has even number of prime factors},
S₂={d| d|N,a≤d≤b,d has odd number of prime factors},
Prove: |S₁|−|S₂|≤C_(k)^((k)/(2))
Original LaTeX notation
Let $k$ be a fixed even positive integer, $N$ is the product of $k$ distinct primes $p_1,...,p_k$, $a,b$ are two positive integers, $a,b\leq N$. Denote 
$S_1=\{d|$ $d|N, a\leq d\leq b, d$ has even number of prime factors$\}$,
$S_2=\{d|$ $d|N, a\leq d\leq b, d$ has odd number of prime factors$\}$,
Prove: $|S_1|-|S_2|\leq C^{\frac{k}{2}}_k$

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task_id
db35740e-a473-5fb5-bbf3-74f4f2067190
task_key
test--db35740e-a473-5fb5-bbf3-74f4f2067190
task_revision_id
1
config / split
/ test

Official source

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