The Binary Root

Algebra Level 5

A quadratic equation

x2px+q=0x^2-px+q=0

is called binary-quadratic if it satisfy the following conditions:

  • All digits of the non-negative integers pp and qq are either 00 or 11

  • All digits of the roots are either 00 or 11

How many binary-quadratic equations are there such that both roots are smaller than 10410^4.

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