Answer:
4
Explanation:
To find the remainder when 2^2222 is divided by 7, we can use Fermat's Little Theorem, which states that if p is a prime number and a is an integer not divisible by p, then a^(p-1) is congruent to 1 modulo p. In this case, p = 7 and a = 2, so we have:
2^6 is congruent to 1 modulo 7 (by Fermat's Little Theorem)
Dividing 2222 by 6 gives a quotient of 370 with a remainder of 2. Therefore:
2^2222 = (2^6)^370 * 2^2
Since 2^6 is congruent to 1 modulo 7, we can simplify the expression:
2^2222 is congruent to 1^370 * 2^2 modulo 7
2^2222 is congruent to 4 modulo 7
Therefore, the remainder when 2^2222 is divided by 7 is 4.