@ARTICLE{NUMBER16.MIZ,
  AUTHOR = {P\k{a}k, Karol},
  TITLE = {Elementary Number Theory Problems. {P}art {XVI}},
  SECTION1 = {Problem 63 -- Construct a member in an arithmetic progression that has a given sequence of digits},
  SECTION2 = {Problem 67 -- Construct an infinite set of relatively prime numbers in a given arithmetic progression},
  SECTION3 = {Problem 68 -- Construct an infinite set of numbers with exactly the same prime divisors in a given arithmetic progression},
  SECTION4 = {Problem 65 -- Construct an arithmetic progression with the least difference without Fibonacci numbers},
  SECTION5 = {Problem 66 -- Construct an arithmetic progression ak+b (k=0,1,2,$\ldots$) without Fibonacci numbers where a,b are coprime.},
  SECTION6 = {Problem 96 -- Find the largest prime number in the sequence 1, 31,331, 3331, $\ldots$},
  SECTION7 = {Product of Different Primes Selected Properties},
  SECTION8 = {Problem 93 -- Prove that the ratio of the smallest prime number that does not divide $n$ to $n$ tends to zero as $n$ increases to infinity},
  SECTION9 = {Problem 95 -- Prove that for all sufficiently large $n,$ between $n$ and $2n$ there exists at least one number which is a product of s different primes for a given s},
  SECTION10 = {Problem 102 -- Prove that Chebyshev theorem is equivalent to the theorem that for integers $n > 1$ the expansion of $n!$ into prime factors contains at least one prime with exponent 1},
  SECTION11 = {Problem 103 -- Prove equivalence, there are two primes between n and 2n where 5 < n, and the expansion of $n!$ into prime factors contains at least two primes with exponent 1 where $n > 11$.},
  DAY = {14},
  MONTH = {December},
  YEAR = {2024},
  ADDRESS1 = {Faculty of Computer Science\\University of Bia{\l}ystok\\ Konstantego Cio{\l}kowskiego 1M, 15-245 Bia{\l}ystok\\Poland},
  SUMMARY = {In this paper another ten problems from \cite{Sierpinski:1970} are formalized,
  using the Mizar formalism \cite{Mizar-State-2015,BancerekJAR:2018,Kornilowicz:2015:FC}, namely: 
  63, 65, 66, 67, 68, 93, 95, 96, 102, 103.}}
