- #1
Ebn_Alnafees
- 7
- 0
Problem 1
Prove that among any 39 consecutive natural numbers
it is always possible to find one whose sum of digits
is divisible by 11.
Problem 2
Sets of 4 positive numbers are made out of each other according
to the following rule: (a, b, c, d) (ab, bc, cd, da).
Prove that in this (infinite) sequence (a, b, c, d) will
never appear again, except when a = b = c = d = 1.
Problem 3
Take a series of the numbers 1 and (-1) with a length
of 2k (k is natural). The next set is made by multiplying
each number by the next one; the last is multiplied by the
first. Prove that eventually the set will contain only ones.
Problem 4
What is the largest x for which
427 + 41000 + 4x
equals the square of a whole number?
Problem 5
Prove that for any prime number p > 2 the numerator m of the fraction
http://
is divisible by p.
Prove that among any 39 consecutive natural numbers
it is always possible to find one whose sum of digits
is divisible by 11.
Problem 2
Sets of 4 positive numbers are made out of each other according
to the following rule: (a, b, c, d) (ab, bc, cd, da).
Prove that in this (infinite) sequence (a, b, c, d) will
never appear again, except when a = b = c = d = 1.
Problem 3
Take a series of the numbers 1 and (-1) with a length
of 2k (k is natural). The next set is made by multiplying
each number by the next one; the last is multiplied by the
first. Prove that eventually the set will contain only ones.
Problem 4
What is the largest x for which
427 + 41000 + 4x
equals the square of a whole number?
Problem 5
Prove that for any prime number p > 2 the numerator m of the fraction
http://
is divisible by p.
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