To use Fermat's Little Theorem to find a number "a" congruent to 71013 modulo 93, then first determine the value of 71013 modulo 92 using the theorem.

Fermat's Little Theorem states that if "p" is a prime number and "a" is any positive integer not divisible by "p," then:

a^(p-1) ≡ 1 (mod p)

In this case, the modulus is 93, which is not prime, so we need to modify the theorem slightly. If "a" and "m" are positive integers such that they are coprime (gcd(a, m) = 1), then:

a^φ(m) ≡ 1 (mod m)

where φ(m) represents Euler's totient function, which gives the count of positive integers less than or equal to "m" that are coprime to "m".

In this case, φ(93) can be calculated by considering the prime factors of 93: 93 = 3 * 31. Since these factors are prime, then apply the formula:

φ(93) = φ(3) * φ(31) = (3-1) * (31-1) = 2 * 30 = 60

Therefore, according to Fermat's theorem:

71013⁶⁰ ≡ 1 (mod 93)

Now, reduce the exponent 71013 modulo 60:

71013 ≡ (60 * 1183) + 33 ≡ 33 (mod 60)

Now, need to find a number "a" between 0 and 92 that is congruent to 33 modulo 60. We can add multiples of 60 to 33 until we obtain a number within the desired range:

33 + 60 = 93 (outside the desired range)

33 + 260 = 153 (outside the desired range)

33 + 360 = 213 (outside the desired range)

33 + 460 = 273 (outside the desired range)

33 + 560 = 333 (outside the desired range)

33 + 660 = 393 (outside the desired range)

33 + 760 = 453 (outside the desired range)

33 + 860 = 513 (outside the desired range)

33 + 960 = 573 (outside the desired range)

33 + 1060 = 633 (outside the desired range)

33 + 1160 = 693 (outside the desired range)

33 + 1260 = 753 (outside the desired range)

33 + 1360 = 813 (outside the desired range)

33 + 1460 = 873 (outside the desired range)

33 + 1560 = 933 (outside the desired range)

33 + 16*60 = 993 (outside the desired range)

Finally, 33 + 17*60 = 1113 falls within the desired range.

Hence, a number "a" that satisfies the congruence 71013 ≡ a (mod 93) is a = 1113.

To summarize, we find that a number "a" congruent to 71013 modulo 93 can be chosen as a = 1113.