What is a lemma?
Lemma and theorem are two different concepts in mathematics and cannot be termed the same.
Answer: A lemma is a proven statement, used to prove other statements.
Let us go through the example to have a better understanding of the given term.
A lemma is nothing but a proven statement that is used to prove other statements. In other words, we can also say that a theorem is a result you're interested in, a corollary is a result that follows from a theorem, and a lemma is a result that you use to prove a theorem.
A lemma is like a mini-theorem that helps you prove a bigger theorem or statement. In other words, it's a small building block to your final destination with respect to proof.
EUCLID'S DIVISION LEMMA:
Euclid's division lemma gives us a systematic procedure to compute the HCF of any two positive integers which is termed as the Euclid division algorithm.
Euclid's division lemma states that for any two positive integers a and b, there exist two unique whole numbers say q and r, such that
a = bq + r , where 0 ≤ r < b
Here, a = Dividend , b = Divisor , q = Quotient , r = Remainder
It can be written as,
Dividend = (Divisor × Quotient) + Remainder
Thus, a lemma is a proven statement, use to prove other proven statements.