Jack and Nancy, delving into the intricate realm of prime numbers, encountered a captivating puzzle woven with the enigmatic equation involving distinct primes a, b, c, and d.
"In this numerical labyrinth," Nancy elucidated, "we are tasked to discern the elusive essence hidden within the equation d = a²b² - 49c²."
"Behold," she continued, "let us unfurl the equation, revealing its hidden layers through the intricate art of factoring."
"The equation unfolds as d = (ab - 7c)(ab + 7c)," Nancy explained, a hint of mystery lingering in her voice. "Evidently, d stands resolute as a prime number, guiding our exploration."
"In the intricate dance of primes, the equation unveils its enigma: ab - 7c must equal 1," she expounded, her words echoing the essence of trial and error that often illuminates such numerical quests.
"Through our journey of exploration," Nancy revealed, "we encounter the luminous solution where the quartet (a, b, c, d) coalesce harmoniously as (3, 5, 2, 29), an epitome of balance in this numerical symphony."
"In this quest for the smallest essence," Nancy concluded, "the sum of the primes a, b, and c unveils itself, resonating as the mysterious minimum value of 10."
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然後按「加至主畫面」