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... tion problems are also difficult, but the difficulty lies in a different direction. The competition problems are very straightforward. Even when asking for integer solutions, they are typically restricted to a specific range, testing the participants’ basic problem-solving skills, and their flexible use of theorems and methods.

Solving his equation, however, directly involves the theoretical depth of modern number theory. Its solution requires more complex algebraic geometry tools, arith ...

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Sold by her father, Bella short for Arabella, was forced to live a life as a slave that would entertain the guests of the castle.The job of slaves were merely to be humiliated and to have as feast once they became a boring creature toward the guests. Arabella with her fierce attitude had only caused more trouble than good, although that helped her from being feasted by the vampires until her body dried up, the vampires also enjoy in harming her, toying with her, hoping to see that one day she would break.However she had caught the wrong attention by those crimson gaze, eventually being the toy of the one and only Mad Crown Prince of Versailles. Eventually this interest only cause her to be more tangled by the twisted and thorny battle for the Throne.Will eventually Bella concede and accept the Mad crown prince?Or will she finally succeed in running away from his grasp.Why her?*** excerpt***Arabella felt her wrists stung as the shackle around her wrist jingled from the sudden pull. She then met with the icy red eyes that brood down upon her appearance, drinking into every inch of her figure as if he was studying her, even to how those breaths escaped her lips.“I thought we had bonded over the days we have spent together, Bella,” he sang, his bright scarlet eyes betraying the singing tone he had used as it had grown so dark and filled with anger. “Yet you left so quickly as soon as I opened the castle gate.”Bella gritted her teeth, her eyes glaring at him as she defiantly shook his hand off her face, “I can remind you if you have forgotten it, Your Majesty, I am kept here against my wish.”Cassius' smile faded as he stared at her. The sudden pin-drop silence filled her nerves with tension as she found his smileless face the most terrifying sight. She had always known his fearsome side however, it felt scarier tonight. Bella tried to endure how loud her heart had raced against her chest, gathering her breaths together even though it remained shallow in his presence.“So cold,” he muttered, his tone trying to tease her, but she could see the raw anger crossing his eyes. “You cannot run from me. Not after what we've done. Not after what you promised.”Her heart faltered. She wasn't supposed to stay in this castle; she knew that the royal palace was filled with those vampire monsters who would kill for their desire, simply to have fun. She knew she should never give her heart to any of these monsters, and she had once believed she would never. But that was until Cassius came.She had made that promise because her heart had betrayed her, and she wished that she had never uttered that promise. Promises she had made to him on the call of love. Yet deep within her, a part of her still crave for him.“You're not the first one I have broken my promises with,” she gritted her teeth and looked up at him, “I broke my promise the way you broke yours first, isn't it fair?”“Fair? Then was everything a lie, Arabella?” he murmured, his hands cupping her face, forcing her to meet his eyes. “You were mine the moment you entered my castle. And you will be mine until the very end.”She gulped as his eyes shone underneath the moonlight, his gaze unforgiving over her, exposing his wild hunger.Her breath caught, her pulse quickening. “A human and a vampire should have never stayed together. They were all right.”“I don't care,” he spoke through his clenched jaw. “You're going to remain here by my side forever.”