A007970: Proof of a Theorem Related to the Happy Number
... d of the Pell equation x2 − d y 2 = +1 for which the positive fundamental solution (x0 , y0 ) has odd y0 . Together with the proof that the products of the 1-happy number couples, A007969, coincide with the d values which have even positive fundamental solution y0 , found as a W. Lang link in A00796 ...
... d of the Pell equation x2 − d y 2 = +1 for which the positive fundamental solution (x0 , y0 ) has odd y0 . Together with the proof that the products of the 1-happy number couples, A007969, coincide with the d values which have even positive fundamental solution y0 , found as a W. Lang link in A00796 ...
Functions and Equations - Iowa State University Department of
... example, 7,120 is divisible by 8 because 120 is divisible by 8, i.e. 8 × 15 = 120. 6. The sum of the digits in all multiples of 9 is 9 or a multiple of 9. 7. All multiples of 10 end in 0. 8. Numerals whose alternating sum of digits is divisible by 11 represent numbers divisible by 11. Consider, for ...
... example, 7,120 is divisible by 8 because 120 is divisible by 8, i.e. 8 × 15 = 120. 6. The sum of the digits in all multiples of 9 is 9 or a multiple of 9. 7. All multiples of 10 end in 0. 8. Numerals whose alternating sum of digits is divisible by 11 represent numbers divisible by 11. Consider, for ...
First Order Linear Differential Equations
... Second order homogenous linear differential equation with constant coefficients The general formula for such equation is To solve this equation we assume the solution in the form of exponential function: ...
... Second order homogenous linear differential equation with constant coefficients The general formula for such equation is To solve this equation we assume the solution in the form of exponential function: ...
