<prompt> Hlalosa mokhoa oa ho sebelisa Theorem e Nyenyane ea Fermat.nan  <response>: Instruction in English: Explain how to use the Fermats Little Theorem. . Response in English: Fermats Little Theorem is an important concept in number theory that is useful in primality testing and modular arithmetic. To use Fermats Little Theorem, you need to understand the basic principles of the theorem and how you can apply it to different problems. Heres a step-by-step explanation on how to use Fermats Little Theorem:1. Understand the theorem: Fermats Little Theorem states that if p is a prime number, then for any integer a, the number ap - a is an integer multiple of p. In other words, ap a mod p.2. Apply the theorem to a problem: Suppose you want to find the remainder when 5200 is divided by 13 i.e. 5200 mod 13. Let p 13, which is prime.3. Rewrite the expression: Here a is 5 so we have by Fermats Little Theorem that 5p 5 mod 13. As 13 is prime, from the theorem we have 513 5mod 13.4. Take powers of both sides: Taking the 15th power of both sides, you get 51315 515 mod 13, so 5195 515 mod 13.5. Combine powers: Now we can quickly calculate 5200 mod 13. Since 5200 55 5195 and 5195 515 mod 13, we have 5200 55 515, which is 3125 3,075,875 8 8 64 -1 mod 13. Thus 5200 mod 13 12.Thats how to use Fermats Little Theorem. Keep in mind that you can only use Fermats Little Theorem if p is a prime number, so always check to make sure that p is prime before applying the theorem. . Response in Sesotho: Fermats Little Theorem ke mohopolo oa bohlokoa oa teori ea lipalo o thusang litekong tsa mantlha le lipalo tsa modular. Ho sebelisa Fermats Little Theorem, o hloka ho utloisisa melao-motheo ea theorem le hore na u ka e sebelisa joang mathateng a fapaneng. Mona ke tlhaloso ea mohato ka mohato ea mokhoa oa ho sebelisa Theorem ea Fermat: 1. Utloisisa khopolo-taba: Fermats Little Theorem e re haeba p ke palo e ka sehloohong, joale bakeng sa palo efe kapa efe a, palo ap - a ke palo e feletseng. bongata ba p. Ka mantsoe a mang, ap a mod p. 2. Sebelisa theorem bothateng: Ha re re u batla ho fumana se setseng ha 5200 e aroloa ka 13 ke hore 5200 mod 13. Let p 13, e leng ea mantlha. 3. Ngola hape poleloana: Mona a ke 5 kahoo re na le Fermats Little Theorem hore 5p 5 mod 13. Kaha 13 ke ea pele, ho tloha ho theorem re na le 513 5 mod 13. 4. Nka matla a mahlakore ka bobeli: Ho nka matla a 15 a mahlakore ka bobeli, u fumana 51315 515 mod 13, kahoo 5195 515 mod 13. 5. Kopanya matla: Hona joale re ka potlakela ho bala 5200 mod 13. Ho tloha 5200 55 5195 le 5195 515 mod 13, re na le 5200 55 515, e leng 3125 3,075,875 8 8 64 -1 mod 13. Kahoo 5200 mod 13 12. Ke mokhoa oa ho sebelisa Fermats Little Theorem. Hopola hore o ka sebelisa Fermats Little Theorem feela haeba p e le nomoro e ka sehloohong, kahoo kamehla hlahloba ho netefatsa hore p ke ea bohlokoa pele u sebelisa theorem. 