Blogs about: Problem Of The Bi Week
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20. Sequences of Consecutive Integers
A37 If is a natural number, prove that the number is not a perfect square. A9 Prove that among any ten consecutive positive integers at least one is relatively prime to the product of the others. O51 … more →
Project PEN
20. Sequences of Consecutive Integers
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cpohoata wrote 7 months ago: A37 If is a natural number, prove that the number is not a perfect square. A9 Prove that among any t … more →
19. Binomial Sum Divisible by Primes
cpohoata wrote 8 months ago: E16 Prove that for any prime in the interval , divides … more →
18. Fractions Mod p and Wolstenholme's Theorem
danielkohen wrote 8 months ago: A23 Prove that if is expressed as a fraction, where is a prime, then divides the numerator. A24 Let … more →
17. A Hidden Divisibility
cpohoata wrote 9 months ago: A13 Show that for all prime numbers , is an integer. … more →
16. Using Quadratic Residues
compactorange wrote 1 year ago: C2 The positive integers and are such that the numbers and are both squares of positive integers. Wh … more →
15. Exponential Congruence Sequence
compactorange wrote 1 year ago: D5. Prove that for , D6. Show that, for any fixed integer the sequence is eventually constant. Sorry … more →
14. Different Approaches to an Intuitive Problem
gorofir wrote 1 year ago: The fourth problem of the second season of PEN is as follows: N17. Suppose that and are distinct rea … more →
13 Minimum prime divisors
compactorange wrote 1 year ago: 13. [PEN A14 A71] A14. Let be an integer. Show that does not divide . A71. Determine all integers su … more →
12. A Generalization of an Identity
compactorange wrote 1 year ago: Here goes the second problem of the second season! 12. PEN I10 Show that for all primes , . … more →
11. Three ways to attack a functional equation
compactorange wrote 1 year ago: Hi everyone. PEN is BACK. Here goes the first problem of the second season! 11. PEN K11 (Canada 2002 … more →
10. Partitions
compactorange wrote 1 year ago: 10. PEN B6 Consider the set of all five-digit numbers whose decimal representation is a permutation … more →
09. Primitive Roots: Revisited
compactorange wrote 1 year ago: 09. PEN B6 Suppose that does not have a primitive root. Show that for every relatively prime to . … more →
08. An arithmetic partition
compactorange wrote 1 year ago: 08. PEN O 35 ( Romania TST 1998 ) Let be a prime number and be integers. Prove that is an arithmetic … more →
07. A combinatorial congruence
compactorange wrote 1 year ago: 07. PEN D2 (Putnam 1991/B4) Suppose that is an odd prime. Prove that … more →
06. A historical divisibility
Yimin Ge wrote 1 year ago: 06. PEN A3 ( IMO 1988 ) Let and be positive integers such that divides . Show that is the square of … more →
05. On the monotonicity of the divisor function.
aimingbeyond wrote 1 year ago: 05a. [Saint-Petersburg 1998] Let denote the number of positive divisors of the number . Prove that t … more →
04. A hidden symmetry
compactorange wrote 1 year ago: O4. PEN I11 (Korea 2000) Let be a prime number of the form . Show that … more →
03. A theorem on sum-free subsets
aimingbeyond wrote 1 year ago: Here goes the problem: 03. PEN O53 (Schur Theorem) Suppose the set is partitioned into disjoint subs … more →
New co-author.
aimingbeyond wrote 1 year ago: We are glad to announce you that starting this week, Andrei Frimu is co-author of Problem of the bi- … more →
