The Number Theory comes back as the heart of unified Science, in a Computing Cosmos using bases 2;3;5;7 whose two symmetric combinations explain main lepton mass ratios. corresponding Holic Principle induces symmetry between Newton and Planck constants which confirm Permanent Sweeping Holography Bang Cosmology, with invariant baryon density 3/10, dark baryons being dephased matter-antimatter os...

Summary This paper reports on the formalization in Mizar system [1], [2] of ten selected problems from W. Sierpinski’s book “250 Problems Elementary Number Theory” [7] (see [6] for details this concrete dataset). article is devoted mainly to arithmetic progressions: 52, 54, 55, 56, 60, 64, 70, 71, and 73 belong chapter “Arithmetic Progressions”, problem 50 “Relatively Prime Numbers”.

Summary This paper reports on the formalization of ten selected problems from W. Sierpinski’s book “250 Problems in Elementary Number Theory” [5] using Mizar system [4], [1], [2]. 12, 13, 31, 32, 33, 35 and 40 belong to chapter devoted divisibility numbers, problem 47 concerns relatively prime whereas 76 79 are taken composite numbers.