# Consecutive is unpredictable (Part 2)

**Number Theory**Level 5

Let \( \large{\color{red}a\color{blue}b\color{purple}c} \) be the last three digits of \( \large{1^{2}+2^{3}+3^{4}+4^{5}+5^{6}+...+998^{999}+999^{1000}} \).

Find \( \large{\color{red}a\color{blue}b\color{purple}c} \) \( mod \) \( 69 \).

**Details:**

The exponents are in a consecutive order of the positive integers: \( 2, 3, 4, ..., 998, 999, 1000 \)

\( \large{\color{red}a\color{blue}b\color{purple}c} \) is three different digits, like \( 346 \), not algebraic expression like \( \large{\color{red}a \times\color{blue}b\times\color{purple}c} \) \( (3\times4\times6) \)

More challenging problems? Here!