<prompt> Ngola mathata a mahlano a tsebahalang haholo a lipalo.nan  <response>: Instruction in English: List five of the most famous mathematics problems. . Response in English: 1. Fermats Last Theorem: The theorem states that no three positive integers a, b, and c can satisfy the equation an bn cn for any integer value of n greater than two. 2. The Riemann Hypothesis: This problem deals with the distribution of prime numbers, and states that all nontrivial zeros of the Zeta function have a real part of 12. 3. The Collatz Conjecture: Also known as the 3n 1 problem, it states that for any positive integer n, the sequence obtained by repeatedly applying the function; n2 if n is even, 3n 1 if n is odd always reaches the number 1. 4. Goldbachs Conjecture: This problem states that every even integer greater than 2 can be expressed as the sum of two prime numbers. 5. The Poincaré Conjecture: This problem deals with topology and the properties of three-dimensional objects. It states that any simply connected, closed 3-manifold is topologically equivalent to the 3-sphere. . Response in Sesotho: 1. Khopolo-taba ea ho Qetela ea Fermat: Khopolo-taba e bolela hore ha ho linomoro tse tharo tse nepahetseng a, b, le c tse ka khotsofatsang equation an bn cn bakeng sa boleng leha e le bofe bo feletseng ba n kholo ho feta tse peli. 2. Khopolo-taba ea Riemann: Bothata bona bo sebetsana le kabo ea linomoro tse ka sehloohong, me e bolela hore li-zero tsohle tse sa tsitsang tsa mosebetsi oa Zeta li na le karolo ea sebele ea 12. 3. Khopolo ea Collatz: E boetse e tsejoa e le bothata ba 3n 1, e bolela hore bakeng sa palo leha e le efe e nepahetseng ea n, tatellano e fumanoang ka ho sebelisa mosebetsi khafetsa; n2 haeba n e lekana, 3n 1 haeba n e le odd e lula e fihla palo ea 1. 4. Khopolo-taba ea Goldbach: Bothata bona bo bolela hore palo e ngoe le e ngoe e kholo ho feta 2 e ka hlalosoa e le kakaretso ea linomoro tse peli tse kholo. 5. Poincaré Conjecture: Bothata bona bo sebetsana le topology le thepa ea lintho tse tharo-dimensional. E bolela hore ntho leha e le efe e hokahaneng, e koetsoeng ka makhetlo a 3 e lekana le 3-sphere. 