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Found: 3

Problems Algebra Algebraic inequalities and systems of inequalities Linear inequalites and systems of inequalities Calculus Number sequences Number sequences (other)

15–16 3.0

Prove that in any infinite decimal fraction you can rearrange the numbers so that the resulting fraction becomes a rational number.

Problem #PRU-65001

Problems Calculus Number sequences Number sequences (other) Number Theory Divisibility The fundamental theorm of arithmetic. Prime factorisation.

12–14 3.0

In a row there are 20 different natural numbers. The product of every two of them standing next to one another is the square of a natural number. The first number is 42. Prove that at least one of the numbers is greater than 16,000.

Problem #PRU-116589

Problems Number Theory Divisibility Divisibility of a number. General properties Algebra Sequences Recurrent relations Linear recurrent relations Calculus Number sequences Number sequences (other)

13–15 3.0

The sequence of numbers \(a_1, a_2, \dots\) is given by the conditions \(a_1 = 1\), \(a_2 = 143\) and

for all \(n \geq 2\).

Prove that all members of the sequence are integers.