Please help me to do this 2 problems?

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Answer 1 · 2017-05-16T13:51:05

See below.

5)
Let $d(n)$ be the function which counts the number of digits of $n$ then

5.1) $n ge 10^(d(n)) ge g(n)$
5.2) $(n-6)^2=g(n)->n = sqrt(g(n))+6$ then
$g(n_k) = k^2, k = 1,2,3,cdots$ so the equation to obey is

$n_k = k+6$ so the only number observing this relationship is

$n_1=7$

6)
Let $4+p_1p_2 = m_1^2$ and $4+p_1p_3=m_2^2$
then

${(p_1p_2=(m_1-2)(m_1+2)),(p_1p_3=(m_2-2)(m_2+2)):}$

but $p_1,p_2,p_3$ being prime numbers then

${(p_1=m_1-2),(p_2=m_1+2),(p_1=m_2+2 " otherwise " m_1=m_2),(p_3=m_2-2):}$

so

$m_1 = m_2+4$ then

${(p_1=p_3+4),(p_2=p_1+4):}$

and

$p_2> p_1 > p_3$

so the prime numbers are

$p_1-4, p_1, p_1+4$

or

$p_3=3, p_1=7, p_2=11$