The ABC Conjecture

As taken from Wikipedia:

The abc conjecture (also known as the Oesterlé-Masser conjecture) is a conjecture in number theory, first proposed by Joseph Oesterlé (1988) and David Masser (1985). It is stated in terms of three positive integers, $a$, $b$ and $c$ (hence the name) that are relatively prime and satisfy $a + b = c$. If $d$ denotes the product of the distinct prime factors of $a \cdot b \cdot c$, the conjecture essentially states that $d$ is usually not much smaller than $c$. In other words: if $a$ and $b$ are composed from large powers of primes, then $c$ is usually not divisible by large powers of primes.

The abc conjecture is well known for the many interesting consequences it entails. Many famous conjectures and theorems in number theory would follow immediately from it. Goldfeld (1996) described the abc conjecture as "the most important unsolved problem in Diophantine analysis."

Several solutions have been proposed. The most recent one is still being evaluated by the mathematical community.

To simplify the rules:

• $a$, $b$, and $c$ are positive integers.
• $a$, $b$, and $c$ are composed of distinct prime factors.

To illustrate the terms, let $a = 16 = 2^4$, $b = 17$, and $c = 16 + 17 = 33 = 3 \cdot 11$. Then $d = 2 \cdot 17 \cdot 3 \cdot 11 = 1122$, which is greater than $c$.

The goal of this problem is to find the exceptions where $c > d$, within a given range for $a$, $b$, and $c$.

The first line of input contains $N$ ($0 < N < 100$), the number of test cases.

Each of the following $N$ lines contains two integers $L$ and $H$ ($2 \le L \le H \le 5000$), the lower and upper bounds of $a$, $b$, and $c$. The constraints are $L \le a, b < c \le H$, and $a \ne b$.

For each test case, output one of the following:

• A line "$a + b = c$" for each equation that satisfies the criteria above. Sort the lines in ascending order by $c$, and then in ascending order by $a$ when several equations share the same $c$.
• A line "No exceptions" if no equation satisfies the criteria.

Each test case is followed by a blank line.