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Found: 3

Problems Algebra Algebraic equations and systems of equations Higher order equations. Palindromic polynomial equations Equations of higher order (other)

11–14 2.0

Solve the equation with integers \(x^2 + y^2 = 4z - 1\).

Problem #PRU-35438

Problems Algebra Algebraic equations and systems of equations Higher order equations. Palindromic polynomial equations Equations of higher order (other) Calculus Real numbers Integer and fractional parts. Archimedean property

2.0

In a group of friends, each two people have exactly five common acquaintances. Prove that the number of pairs of friends is divisible by 3.

Problem #PRU-78244

Problems Algebra Absolute value Absolute value of a number (other) Number Theory Numeral systems Decimal number system Algebraic equations and systems of equations Higher order equations. Palindromic polynomial equations Equations of higher order (other)

11–13 4.0

Two people play a game with the following rules: one of them guesses a set of integers \((x_1, x_2, \dots , x_n)\) which are single-valued digits and can be either positive or negative. The second person is allowed to ask what is the sum \(a_1x_1 + \dots + a_nx_n\), where \((a_1, \dots ,a_n)\) is any set. What is the smallest number of questions for which the guesser recognizes the intended set?