# Recurrences and Divisors

Given that $$\mathrm{a_0 = b_0 = 0}$$
$$\mathrm{a_i , b_i \geq 0}$$ .......... $$\forall i\geq 0$$
$$\mathrm{a_1 : b_1 = 6:61}$$
$$\mathrm{b_1^2-a_1^2 = 3685}$$
$$\mathrm{a_n = 8a_{n-1} - 7a_{n-2}}$$
$$b_n = 65b_{n-1}- 126 b_{n-2}$$

Find the Greatest Common Divisor of

the numbers formed by last 5 digits of $$\mathrm{\text{a}_{2560}}$$ and $$\mathrm{b_{1000}}$$

Details And Assumptions :-

The last five digits are taken in order as they appear i.e.

number formed by last 5 digits of the number 67865783658 is 83658 .

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