Prove That the Equation $2 x ^ { 2 } + y ^ { 2 } = 14$

question 90

Essay

Prove that the equation $2 x ^ { 2 } + y ^ { 2 } = 14$ has no positive integer solutions.

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Definitions:

Economies of Scale

The financial benefits businesses receive from their operational scale, where the cost for each unit produced tends to decrease as the scale of production increases since fixed costs are allocated over a greater quantity of output.

Preemption

A strategy or action taken to prevent an opponent from taking an action by being the first to act or by securing a strategic advantage.

Payoff Matrices

A table that shows the potential outcomes or payoffs in a game for each combination of players' strategies.

Repeated Game

A strategic scenario in which the same game is played multiple times, allowing players to adjust their strategies based on past outcomes.